Mohammed Amin Assenine

Boumediene Haddad

Annalisa Paolone

Silvia Antonia Brandán
email: silvia.brandan@fbqf.unt.edu.ar

Didier Villemin

Mostefa Boumediene

Mustapha Rahmouni

Serge Bresson

Experimental and DFT studies on structure, spectroscopic and thermal properties of N-Methyl-N,N,N-trioctylammonium chloride ionic liquid

Keywords: Aliquat 336, ionic liquid, FT-IR, FT-Raman, thermal analysis, DFT calculations

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The interesting physicochemical properties and applications that present the ionic liquids (ILs) have allowed the gradual growth in the investigations of these species from different points of view [START_REF] Watanabe | Application of ionic liquids to energy storage and conversion materials and devices[END_REF][START_REF] Qiang | Experimental and theoretical studies of four allylimidazolium-based ionic liquids as green inhibitors for copper corrosion in sulfuric acid[END_REF][START_REF] Dedzo | Molecular control of the functional and spatial interlayer environment of kaolinite by the grafting of selected pyridinium ionic liquids[END_REF][START_REF] Haddad | Influence of methyl and propyl groups on the vibrational spectra of two imidazolium ionic liquids and their non-ionic precursors[END_REF][START_REF] Haddad | Effects of C (2) methylation on thermal behavior and interionic interactions in imidazolium-based ionic liquids with highly symmetric anions[END_REF][START_REF] Ni | One-step conversion of biomassderived furanics into aromatics by Brønsted acid ionic liquids at room temperature[END_REF][START_REF] Nawała | Applications of ionic liquids in analytical chemistry with a particular emphasis on their use in solid-phase microextraction, Trac-Trend[END_REF][START_REF] Zhou | Separation of thioglycolic acid from its aqueous solution by ionic liquids: Ionic liquids selection by the COSMO-SAC model and liquid-liquid phase equilibrium[END_REF][START_REF] Kausteklis | Cation-anion interactions in 1buthyl-3-methyl imidazolium nitrate ionic liquid and their effect on their structural and vibrational properties[END_REF][START_REF] Bystrzanowska | How green are ionic liquids?-A multicriteria decision analysis approach[END_REF][START_REF] Pei | Aggregation Behavior of Pyrrolidinium Ionic Liquid Surfactants in-OH-Functionalized Ammonium-Based Protic Ionic Liquids[END_REF][START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF][START_REF] Gildeh | Experimental and theoretical probing of the physicochemical properties of ionic liquids composed of [Bn-DBU]+ cation and various anions[END_REF][START_REF] Haddad | Bidentate cation-anion coordination in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate supported by vibrational spectra and NBO, AIM and SQMFF calculations[END_REF]. For instance, the quaternary ammonium salt, known as Aliquat 336, presents characteristics properties and major applications [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF][START_REF] Semghouni | Chromium (VI) removal by Aliquat-336 in a novel multiframe flat sheet membrane contactor[END_REF][START_REF] J P Mikkola | Aliquat 336®-a versatile and affordable cation source for an entirely new family of hydrophobic ionic liquids[END_REF][START_REF] S K Panja | Clusters of the Ionic Liquid 1-Hydroxyethyl-3-methylimidazolium Picrate: From Theoretical Prediction in the Gas Phase to Experimental Evidence in the Solid State[END_REF][START_REF] Liu | An investigation of trioctylmethylammonium ionic liquids by X-ray photoelectron spectroscopy: The cation-anion interaction[END_REF][START_REF] Mateescu | The application of aliquat 336 as carrier in processes for wastewater treatment containing heavy metals[END_REF]. Besides, the synthesis reactions of these ionic liquids are environmentally benign and friendly due to its stability against air and moisture and; in addition, these salts are easy to handle [START_REF] Semghouni | Chromium (VI) removal by Aliquat-336 in a novel multiframe flat sheet membrane contactor[END_REF][START_REF] J P Mikkola | Aliquat 336®-a versatile and affordable cation source for an entirely new family of hydrophobic ionic liquids[END_REF][START_REF] Mateescu | The application of aliquat 336 as carrier in processes for wastewater treatment containing heavy metals[END_REF]. Studies on Aliquat 336 containing chloride anion have suggested that its use is limited by the strong coordination effect of that halogen [START_REF] J P Mikkola | Aliquat 336®-a versatile and affordable cation source for an entirely new family of hydrophobic ionic liquids[END_REF]. Hence, the cation-anion interactions play a very important role in the properties of ILs [START_REF] Haddad | Influence of methyl and propyl groups on the vibrational spectra of two imidazolium ionic liquids and their non-ionic precursors[END_REF][START_REF] Haddad | Effects of C (2) methylation on thermal behavior and interionic interactions in imidazolium-based ionic liquids with highly symmetric anions[END_REF][START_REF] Kausteklis | Cation-anion interactions in 1buthyl-3-methyl imidazolium nitrate ionic liquid and their effect on their structural and vibrational properties[END_REF][START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF]. Currently, the elucidations of all types of interactions in ILs are carried out combining theoretical calculations with different spectroscopic techniques [START_REF] Kausteklis | Cation-anion interactions in 1buthyl-3-methyl imidazolium nitrate ionic liquid and their effect on their structural and vibrational properties[END_REF][START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF][START_REF] Haddad | Bidentate cation-anion coordination in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate supported by vibrational spectra and NBO, AIM and SQMFF calculations[END_REF][START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. So far, various quaternary ammoniums ILs with different cations and anions have been reported for Aliquat 336, including a recent study on the synthesis and structural and thermal properties of [Aliquat + ][NTF 2 -] IL [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF][START_REF] Semghouni | Chromium (VI) removal by Aliquat-336 in a novel multiframe flat sheet membrane contactor[END_REF][START_REF] J P Mikkola | Aliquat 336®-a versatile and affordable cation source for an entirely new family of hydrophobic ionic liquids[END_REF][START_REF] S K Panja | Clusters of the Ionic Liquid 1-Hydroxyethyl-3-methylimidazolium Picrate: From Theoretical Prediction in the Gas Phase to Experimental Evidence in the Solid State[END_REF][START_REF] Liu | An investigation of trioctylmethylammonium ionic liquids by X-ray photoelectron spectroscopy: The cation-anion interaction[END_REF][START_REF] Mateescu | The application of aliquat 336 as carrier in processes for wastewater treatment containing heavy metals[END_REF][START_REF] Domańska | Physicochemical properties and solubility of alkyl-(2hydroxyethyl)-dimethylammonium bromide[END_REF][START_REF] Aparicio | Study on hydroxylammonium-based ionic liquids I[END_REF][START_REF] Bodo | Structure of the molten salt methyl ammonium nitrate explored by experiments and theory[END_REF][START_REF] L F Faria | Thermal analysis and Raman spectra of different phases of the ionic liquid butyltrimethylammoniumbis (trifluoromethylsulfonyl) imide[END_REF][START_REF] Vitucci | Stabilization of different conformers of bis (trifluoromethanesulfonyl) imide anion in ammonium-based ionic liquids at low temperatures[END_REF][START_REF] M S Miran | Binary protic ionic liquid mixtures as a proton conductor: high fuel cell reaction activity and facile proton transport[END_REF][START_REF] Palumbo | A study of the conformers of the N, N-diethyl-N-methyl-N-propylammonium ion by means of infrared spectroscopy and DFT calculations[END_REF][START_REF] Capitani | Heterogeneity of propyl-ammonium nitrate solid phases obtained under high pressure[END_REF][START_REF] Lima | Comparing two tetraalkylammonium ionic liquids. I. Liquid phase structure[END_REF][START_REF] Haddad | Synthesis, conductivity, and vibrational spectroscopy of tetraphenylphosphoniumbis (trifluoromethanesulfonyl) imide[END_REF][START_REF] Niemann | Cationic clustering influences the phase behaviour of ionic liquids[END_REF] but the structural, electronic, vibrational and topological properties of [Aliquat + ][Cl -] IL was no reported yet. Hence, the aims of this work are: (i) to optimize the structure of [Aliquat + ][Cl -] IL in order to predict structural, electronic, topological and vibrational properties, (ii) to find the coordination mode between cation and anion by using natural bond orbital (NBO) and atoms in molecules (AIM) calculations, (iii) to characterize experimentally [Aliquat + ][Cl -] IL by using the infrared, Raman, 1 H-and 13 C-NMR spectra and, (vi) to perform comparisons of this IL with the reported for [Aliquat + ][NTF 2 -] IL [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. In this work, the experimental infrared (FTIR/ATR) and Raman spectra of [Aliquat + ][Cl -] IL were recorded and its structure in gas phase was optimized by using the B3LYP/6-31G* method [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF][START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF]. Then, the structure of it was confirmed by using 1 H, 13 C and 19 F-NMR spectroscopies. The combinations of vibrational spectra with the DFT calculations and the scaled mechanical force field (SQMFF) methodology have allowed the determination of harmonic force field and the scaled force constants [START_REF] Pulay | Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (QM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene[END_REF][START_REF] Rauhut | Transferable Scaling Factors for Density Functional Derived Vibrational Force Fields[END_REF][START_REF] Sundius | Scaling of ab-initio force fields by MOLVIB[END_REF]. The normal internal coordinates for the cation were taken of those proposed for [Aliquat + ][NTF 2 -] IL [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF] while the used transferable scaling factors were those recommended for the method employed by Rauhut and Pulay [START_REF] Rauhut | Transferable Scaling Factors for Density Functional Derived Vibrational Force Fields[END_REF]. The investigations of reactivity and behaviours of [Aliquat + ][Cl -] IL were evaluated taking into account the frontier orbitals and some interesting descriptors [START_REF] Kausteklis | Cation-anion interactions in 1buthyl-3-methyl imidazolium nitrate ionic liquid and their effect on their structural and vibrational properties[END_REF][START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF][START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. Then, all obtained properties were compared with compounds with similar cations [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF] while the complete assignments of 237 vibration modes expected for [Aliquat + ][Cl -] IL were reported for first time in the present work.

Experimental

Materials and methods

The chemicals used in this study are N-Methyl-N,N,N-trioctylammonium chloride (> 99%) and lithium bis (trifluoromethylsulfonyl) Imide (99%). They were purchased from Aldrich

General procedure for the synthesis of Aliquat 336 ILs

Firstly, the quaternary ammonium salt ([Aliquat + ][Cl -]) is obtained commercially and was used as received. Before use ([Aliquat + ][Cl -]) was dried in phosphorus pentoxide, P 2 O 5 , to remove residual water. The water content was below 300 ppm; this measure was carried out by coulometric Karl Fischer titration performed by means of a Metrohm 831.

NMR analysis

The structure of investigated IL ([Aliquat + ][Cl -]) was checked by NMR in order to probe the desired structure and confirm their purity. 1 H-NMR (400 MHz) and 13 C NMR (100.6 MHz) spectra were recorded on a DRX 400 MHz spectrometer (400 MHz). The chemical shifts (δ) are given in ppm and referred to the internal solvent signal namely tetramethylsilane (TMS) and CDCl 3 .

Thermal analysis

Concomitant measurements of thermogravimetry (TGA) and differential thermal analysis (DTA) were performed by means of a Setaram Setsys Evolution 1200 TG System, with a fixed temperature rate of 5°C/min, in an argon flux of 60 ml/min. For each sample, an initial mass of ~20 mg was used.

Vibrational spectroscopy

FTIR/ATR measurements

The FTIR/ATR measurements were acquired on a Bruker Vertex II-70RAM Spectrometer (Bruker Analytical, Madison, WI) operating with a Golden Gate diamond ATR accessory TM (Specac Ltd, Slough, United Kingdom). The FTIR/ATR spectra were collected with 1 cm -1 nominal resolution by co-adding 64 scans for each spectrum in the range 600-4000 cm -1 . The OPUS Software 6.0 for Windows was used for the management of the instrument.

FT-RAMAN measurements

FT-RAMAN spectra were acquired on a Vertex 70-RAM II Bruker FT-Raman spectrometer. This instrument is equipped with a Nd:YAG laser (yttrium aluminium garnet crystal doped with triply ionized neodymium) with a wavelength of 1064 nm and a maximum power of 1.5 W. The measurement accessory is pre-aligned: only the Z-axis of the scattered light is adjusted to set the sample in the appropriate position regarding the local measurement point.

The RAM II spectrometer is equipped with a liquid nitrogen cooled Ge detector. FT-Raman spectra were collected with 1 cm -1 resolution by co-adding 128 scans for each spectrum at room temperature in the range 45-4000cm -1 . The OPUS 6.0 software was used for the spectral acquisition, manipulation and transformation. These both measurements FTIR/ATR and FT-RAMAN were performed in the Walloon Agricultural Research Center (Craw) Belgium.

Computational details

The modelled of [Aliquat + ][Cl -] was carried out with the GaussView program [START_REF] Nielsen | User´s Reference[END_REF] while its optimization in gas phase was performed by using the functional hybrid B3LYP/6-31G* level of theory with the Revision A.02 of Gaussian 09 program [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF][START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF][START_REF] Gaussian | [END_REF]. The determination of properties of [Aliquat + ][Cl -] in gas phase were evaluated by using the natural bond orbital (NBO), the Bader's theory of atoms in molecules (AIM) 2000 programs [START_REF] Glendening | NBO 3.1[END_REF][START_REF] Bader | Atoms in Molecules, A Quantum Theory[END_REF][START_REF] Biegler-Köning | AIM2000; A Program to Analyze and Visualize Atoms in Molecules[END_REF] and atomic charges derived from semiempirical methods [START_REF] Besler | Atomic charges derived from semiempirical methods[END_REF]. The frontier orbitals were used to obtain the energy gap values while with these parameters were computed the chemical potential (μ), electronegativity (χ), global hardness (η), global softness (S), global electrophilicity index (ω) and global nucleophilicity index (E) descriptors [START_REF] Kausteklis | Cation-anion interactions in 1buthyl-3-methyl imidazolium nitrate ionic liquid and their effect on their structural and vibrational properties[END_REF][START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF][START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. After that, the complete vibrational assignments of [Aliquat + ][Cl -] was performed by using the scaled mechanical force field (SQMFF) procedure with the normal internal coordinates of cation taken of Ref [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF] for

[Aliquat + ][NTf 2 -
] IL and with the Molvib program [START_REF] Pulay | Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (QM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene[END_REF][START_REF] Rauhut | Transferable Scaling Factors for Density Functional Derived Vibrational Force Fields[END_REF][START_REF] Sundius | Scaling of ab-initio force fields by MOLVIB[END_REF]. Potential energy distribution (PED) contributions  10 % and transferable scaling factors were employed to perform the vibrational assignments of IL [START_REF] Rauhut | Transferable Scaling Factors for Density Functional Derived Vibrational Force Fields[END_REF]. To a better correlation the Raman spectra predicted in activities were corrected to intensities by using typical equations [START_REF] Keresztury | Vibrational spectra of monothiocarbamates-II. IR and Raman spectra, vibrational assignment, conformational analysis and ab initio calculations of S-methyl-N,N-dimethylthiocarbamate[END_REF][START_REF] Michalska | The prediction of Raman spectra of platinum(II) anticancer drugs by density functional theory[END_REF]. Finally, the ultraviolet-Visible and 1 H and 13 C NMR spectra were predicted by using Time-dependent DFT calculations (TD-DFT) together and the GIAO method at the same level of theory [START_REF] Ditchfield | Self-consistent perturbation theory of diamagnetism. I. A gage-invariant LCAO (linear combination of atomic orbitals) method for NMR chemical shifts[END_REF].

The volume calculations of cation and IL were computed the Moldraw program [46]. The calculations in solution were performed by using a methodology similar to other ionic liquids [START_REF] Kausteklis | Cation-anion interactions in 1buthyl-3-methyl imidazolium nitrate ionic liquid and their effect on their structural and vibrational properties[END_REF][START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF]. Moreover, the 13 C-NMR spectrum of ([Aliquat + ][Cl -]) was found to have eight signals over the range δ= 0 -65 ppm confirming the presence of the hydrocarbon skeleton.

Results and discussion

NMR results

The spectroscopic data are given below and the H and C atom labeling and the corresponding spectra are shown in Figure 1 (a andb).

[Aliquat + ][Cl -]: 1 H-NMR (400 MHz, (CDCl 3 ) δ H (ppm)= 3.14-3.18 (N + -(CH 2 ) n -, 6H), 2.98

(N + -CH 3 ,3H), 1.64 (N + -(CH 2 )--(CH 2 )-, 6H), 1.

Computational results

Geometrical parameters

Optimized structures of [Aliquat + ][Cl -] and its cation in gas phase by using the B3LYP/6-31G* method can be seen in Figure 2 while in Table 1 are reported the uncorrected and corrected energy values by zero point vibrational energy (ZPVE) for those two species together with the dipole moment values and volumes by using the B3LYP/6-31G* method. The results show that the incorporation of Cl anion to cation generates a higher dipole moment value and a slight increase in the volume, with an expansion in the volume of 39.3 Å 3 . However, the position and orientation of dipole moment vector of [Aliquat+][Cl-] ionic liquid in gas phase by using the B3LYP/6-31G* level of theory is different from that observed for the cation, as shown in Figures 3a and3b. Thus, in the cation the vector is orientated from The values predicted for closest H6-Cl81, H31-Cl81 and H78-Cl81 distances between cation and anion these are distances between the Cl anion and the H atoms of CH 3 (H78) and two next CH 2 groups (H6 and H31) of cation, they are respectively 2.423, 2.380 and 2.404 Å, higher than the value 1.81 Å obtained computationally for the protic analogue of the [Aliquat + ] cation [START_REF] Haque | Ntrioctylammonium chloride as a novel and green corrosion inhibitor for mild steel in an acid chloride medium: electrochemical, DFT and MD studies[END_REF][START_REF] Dong | Mechanism studies on thermal dissociation of tri-n-octylamine hydrochloride with FTIR, TG, DSC and quantum chemical methods[END_REF]. The distance between both N1 and Cl81 atoms is 3.661 Å.

Obviously, in solution the H6-Cl81, H31-Cl81 and H78-Cl81 distances of interactions increase at 2.783, 2.881 and 2.779 Å, respectively.

Atomic charges, molecular electrostatic potentials (MEP) and bond orders

Cation-anion interactions of [Aliquat + ][Cl -] IL were studied in gas phase by using the hybrid B3LYP/6-31G* method and the atomic Mulliken, Merz-Kollman (MK) and NPA charges, molecular electrostatic potentials (MEP) and bond orders (BO), expressed as Wiberg indexes.

The results only for the involved atoms in cation-anion interactions of IL, these are the N1, C5, C30, C77, H6, H31, H78 and Cl81 atoms are presented in Table S1 of Other interesting properties analyzed in both species are the bond orders (BO) expressed as Wiberg indexes which can be seen in Table S1. The BO values of N1 in both [Aliquat + ][Cl -] IL and its cation practically are constant while change slightly the values for the other atoms.

Here, a very important resulted is observed in the BO value for the Cl atom because it is 0.277, which reveals the important coordination modes that it atom present. Thus, when the

NBO and AIM studies

The above studies have evidenced clearly that the Cl atom is tri-coordinate to cation by means ] [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. These interactions correspond to those ionic predicted previously by MK charges and bond orders, supporting newly the characteristics ionic of these interactions.

The second analysis by AIM program using the topological properties and the Bader's theory of atoms in molecules is useful to investigate the characteristic or nature of intra-molecular, H bonds, ionic and covalent polar interactions [START_REF] Bader | Atoms in Molecules, A Quantum Theory[END_REF][START_REF] Biegler-Köning | AIM2000; A Program to Analyze and Visualize Atoms in Molecules[END_REF]. Then, the electron density, ( other ionic one in addition to those three ionic predicted also by NBO analysis.

Frontier orbitals and global descriptors analyses

The ] IL. This study shows that the properties of an IL formed by the [Aliquat + ] cation are strongly dependent of anion.

Thermal analysis

The thermal stability of [Aliquat + ][Cl -] studied in this work were investigated by means of concomitant TGA/DTA measurements (see Figure 6). This IL is thermally stable up to ≈210

°C. The corresponding DTA signal shows an endothermic peak, attributed and confirm to the thermal decomposition. Differently from Mikkola el al [START_REF] J P Mikkola | Aliquat 336®-a versatile and affordable cation source for an entirely new family of hydrophobic ionic liquids[END_REF], it seems that decomposition of this IL occurs at a higher temperature compared to the same cation [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. The determination of harmonic force field of IL was performed with the scaled quantum mechanical force field (SQMFF) procedure taking into account the normal internal coordinates of cation, transferable scaling factors and the Molvib program [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF][START_REF] Pulay | Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (QM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene[END_REF][START_REF] Rauhut | Transferable Scaling Factors for Density Functional Derived Vibrational Force Fields[END_REF][START_REF] Sundius | Scaling of ab-initio force fields by MOLVIB[END_REF]. Here, the quaternary N atom of IL was considered with C 3V symmetry, as in the definition of normal internal coordinates of cation [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF] while a monodentate coordination between cation and anion was proposed for IL because the only interaction with higher energy and lower distance is the C30-H31•••Cl81 interaction. In Table 2 are summarized observed and calculated wavenumbers and assignments for the [Aliquat + ][Cl -] IL and its cation in gas phase by using the hybrid B3LYP Method. Then, assignments for the most important groups are discussed below. 3060 and 3026 cm -1 while the symmetric one at 2875 cm -1 , hence, these modes are assigned to the shoulders observed in Raman at 3067 and 2880 cm -1 , respectively. Note that the antisymmetric stretching modes of remain CH 3 groups of both species are predicted combined with anti-symmetric modes of CH 2 groups. In Table 2 are presented the descriptions of these modes together with their corresponding assignments based on the SQM calculations. Table 2 shows clearly that in this region the positions and assignments of bands corresponding to CH 2 and CH 3 groups in the IL are different from the corresponding to cation due to effect of Cl anion that shift the bands at lower wavenumbers, as observed in the antisymmetric CH 3 stretching modes ( a CH 3 (C77)). Besides, the anti-symmetric CH 2 mode of C30 atom linked to H31 in the IL is predicted at 2994 cm -1 while in the cation it mode is predicted at 2980 cm -1 . In this case in particular is notable the effect of Cl atom in the IL.

4.4.1.2. 1500-1000 cm -1 region. In this region, the effect of Cl also has influence on the positions of bands and assignments of IL, as compared with the cation. Thus, the SQM calculations predict the deformation, wagging and rocking modes of CH 2 groups and, the antisymmetric and symmetric deformation and rocking modes of CH 3 groups for the cation different from those for the IL, as shown in Table 2. Here, in the 1508-1381 cm -1 region it is possible to observe coupling in the deformation modes of both groups. Therefore, the bands and shoulders observed in the IR and Raman spectra in that region are assigned to those deformation modes. The wagging modes of CH 2 groups for cation and IL are predicted from 1432 up to 1230 cm -1 while the rocking modes between 1423 and 1166 cm -1 and, for these reasons, these vibration modes can be assigned according to the SQM calculations and to assignments for species with similar groups [START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF][START_REF] Haddad | Bidentate cation-anion coordination in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate supported by vibrational spectra and NBO, AIM and SQMFF calculations[END_REF][START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. In the cation, the rocking modes of CH 3 groups are predicted between 1188 and 1083 cm -1 while in the IL between 1195 and 1080 cm -1 . Also, in the cation, between 920 and 865 cm -1 are predicted other rocking modes while in the IL between 926 and 875 cm -1 . Consequently, the bands observed in both IR and Raman spectra in those regions are assigned to rocking modes. In addition in this region, C-C stretching modes and CCC and NC 3 deformation modes are predicted for both species by SQM calculations. 3. Here, the H31•••Cl81 stretching mode is predicted by SQM calculations at 67 cm -1 , for which, it mode can be assigned to the shoulder observed in the Raman spectrum at 72 cm -1 .

Force Fields

In this work, the determination of harmonic force field of [Aliquat + ] [Cl -] IL in the gas phase was computed with the SQMFF methodology and the Molvib program by using the B3LYP/6-31G* method while, for the cation it was taken of a previous work reported for the

[Aliquat + ][NTf 2 -
] IL in gas phase at the same level of theory [START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF]. Then, the scaled force constants for both species were calculated from their corresponding force fields and compared with reported for the [BMIM][OTF] IL and its cationic species in Table 3 [START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF]. Regarding first the force constants of [Aliquat + ] [Cl -] IL and its cation, it is observed higher values in the f(N-CH 3 ), f(N-C 3 ), f(CH 2 ) and f(CH 3 ) force constants of cation, as compared with the corresponding to IL because the presence of Cl anion with higher electronegativity in the IL produces three new ionic H•••Cl81 bonds decreasing the forces of other bonds, as was evidenced by NBO and AIM studies. Then, the effect of anion is higher in the quaternary N linked to the three side chains, as compared with the corresponding to N-CH 3 group. A very important observation is that despite of three larges side chains present in [Aliquat + ] and IL the values of f(CH 2 ), f(CH 3 ), f(CH 2 ) and f(CH 3 ) force constants are practically the same for both species and only slight differences are observed due to Cl in IL.

When the values are compared with the [BMIM][OTF] IL and its cation we observed higher values in the f(N-CH 3 ) force constant of these two species because the N atoms are linked to rings [START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF].

Conclusions

In this work, the [Aliquat + ][Cl -] IL was structural and vibrationally characterized combining

Scheme 1 :

 1 Scheme 1: Structure of investigated IL [Aliquat + ][Cl -].

Figure 1 (Figure 1 .

 11 Figure 1 (a and b) shows the NMR spectra versus chemical shift dissolved in (CDCl 3 ) over the scan range 0 to 10 𝛿 ppm for 1 H NMR and from 0 to 150 𝛿 ppm for 13 C NMR for [Aliquat + ][Cl -] IL. 1 H and 13 C-NMR spectra indicates and confirm the absence of any impurities in our investigated IL.

Figure 2 .

 2 Figure 2. Optimized structures of [Aliquat + ][Cl -] and its cation by using the B3LYP/6-31G* method.

  the N atom in direction to N-CH 3 group while in the IL it is oriented from the N atom but in the opposite direction, as clearly shows the Fig. 3b. Hence, the Cl anion modifies in notable form the properties of cation. Main moieties of [Aliquat + ][Cl -] IL and its cation showing the atoms labelling and the N, C, H and Cl atoms involved in cation-anion interactions are shown in Figure S1 of supporting material. The calculations performed in solution by using the PCM method evidence a compression in the volume and an increase in the dipole moment value (18.8 D).

Figure 3a .

 3a Figure 3a. Orientation and direction of dipole moment vector corresponding to cation of [Aliquat + ][Cl -] ionic liquid in gas phase by using the B3LYP/6-31G* level of theory.

Figure 3b .

 3b Figure 3b. Orientation and direction of dipole moment vector of [Aliquat + ][Cl -] ionic liquid in gas phase by using the B3LYP/6-31G* level of theory.

Figure S2 .

 S2 Figure S2. This latter figure shows that the three types of charges on the atoms of both species present practically the same behaviours, however, the MK charges on the [Aliquat + ][Cl -] IL shows a significant difference, as compared with the other ones. The MK charge on N1 has a positive sign in cation while the other two charges on this atom present negative signs. Hence, the presence of Cl atom in the IL produces that MK charge on N1 become negative. In the same way, the MK charges on C5 and C30 have positive signs while the other two charges evidence negative values on these atoms of both species. These changes in the signs of charges on the C atoms obviously modify the values and signs of MK charges on the H6, H31 and H78 atoms. Thus, the MK charge on H6 atom has negative sign while on the H31 presents positive sign in the IL. These studies clearly reveal that the MK charges show differences between the IL and its cation due to the presence of Cl and to interactions cation-anion, for these reasons, these atomic MK charges could explain the different properties between both species.

  Wiberg bond index matrix in the NAO basis values are analyzed we observed that the BO values for the H6, H31 and H78 are respectively of 0.0533, 0.0572 and 0.0545 while for the C5, C30 and C77 are respectively of 0.0245, 0.0269 and 0.0270 whose total value is 0.243, a few lower than the total by atom of 0.277. This way, the C5-H6, C30-H31 and C77-H78 bonds are engaged in certain form in cation-anion interactions. These important results evidence three ionic bonds between IL and its cation through the chlorine atom. The graphic with the Moldraw program presented in Figure4shows a tridentate coordination mode of Cl atom to cation in the [Aliquat + ][Cl -] IL[46].

Figure 4 .

 4 Figure 4. Coordination modes of Cl atoms to cation in the [Aliquat + ][Cl -] IL.

  , the Laplacian values,  2 (r), the eigenvalues (1, 2, 3) of the Hessian matrix and, the |λ1|/λ3 ratio have been calculated in the bond critical points (BCPs) and ring critical points (RCPs) for the [Aliquat + ][Cl -] IL in gas phase by using the B3LYP/6-31G* method. In the cation of IL in gas phase are not observed new interactions while in the IL are observed six interactions (BCPs) which origin six RCPs and one cage critical point (CCP). The CCP is formed when several rings form a cage (see point green colour). The new interactions have different characteristics because the C8-H10•••H80 and C77-H79•••H35 interactions are of H bonds while the other four C5-H6•••Cl81, C30-H31•••Cl81, C77-H78•••Cl81 and C39-H40•••Cl81 are ionic interactions and, all of them can be clearly observed in Figure 5.

Figure 5 .

 5 Figure 5. Molecular graphic for the [Aliquat + ][Cl -] IL in gas phase showing the geometry of all their bond critical points (BCPs), ring critical points (RCPs) and cage critical point (CCP) by using the B3LYP/6-31G* method.

Figure 6 :

 6 Figure 6: TGA and DTA curves of ([Aliquat + ][Cl -]) IL.

Figure 7 .

 7 Figure 7. Experimental Infrared spectra of [Aliquat + ] [Cl -] IL in solid phase compared with the predicted for the cation and IL in gas phase by using the hybrid B3LYP method.

Figure 8 .

 8 Figure 8. Experimental Raman spectra of [Aliquat + ] [Cl -] IL in solid phase compared with the predicted for the cation and IL in gas phase by using the hybrid B3LYP method.

4. 4 . 1 . 3 .

 413 1000-10 cm -1 region. For cation and IL, C-C, N-C stretching and twisting modes of CH 2 and CH 3 groups are expected in this region together with the H31•••Cl81 stretching mode. In the cation, the N-CH 3 stretching mode is predicted at 958 cm -1 while in the IL at 949 cm -1 due to the presence of Cl anion. Hence, the weak Raman band at 959 cm -1 is assigned to that vibration mode of cation and to anti-symmetric N-C stretching mode of IL. The three N-C stretching modes considered with C 3V symmetries are predicted at 844, 801 and 758 cm -1 in the cation while in the IL at 850, 801 and 766 cm -1 . Note that the NC 3 deformation modes of cation and IL are predicted and assigned in practically the same regions. In cation and IL, the twisting CH 2 modes of different groups are predicted by SQM calculations in different regions while the three twisting CH 3 modes in both species are predicted in the same regions (234-213 cm -1 ) although the  w CH 3 (C77) appear coupled with other modes in the IL, as detailed in Table

  experimental FT-IR, FT-Raman and 1 H-and13 C-NMR spectroscopies with theoretical studies based on hybrid B3LYP/6-31G* method. The theoretical structure of [Aliquat + ][Cl -] IL determined in gas phase has shown tree ionic H•••Cl bonds but only one of them with higher energy and lower distance between the involved atoms, as supported by atomic MK charges, bond orders, NBO and AIM calculations. Hence, monodentate coordination between the [Aliquat + ] cation and Cl anion has been proposed to perform the vibrational assignments. The confirmation of optimized structure by NMR measurements has allowed the complete assignments of all bands observed in the infrared and Raman spectra with the aid of SQMFF methodology and the normal internal coordinates. The thermal stability shows that [Aliquat + ][Cl -] start to decompose just above 200°C. The mapped MEP surface evidence a strong concentration of charges around the chloride anion compatible with nucleophilic sites in these regions while the frontier orbital analyses suggest that IL is most reactive than the cation probably due to the low values of both global electrophilicity and nucleophilicity indexes. Comparisons of gap values between [Aliquat + ][Cl -] and [Aliquat + ][NTf 2 -] ILs show that the IL containing chloride is most reactive than the other one suggesting that the properties of an IL containing [Aliquat + ] are strongly dependent of anion. In addition, the scaled force constants for the [Aliquat + ][Cl -] IL are reported while the comparisons with the corresponding to cation evidence the effect of Cl anion on its values.

Figure Captions Scheme 1 :

 1 Figure CaptionsScheme 1: Structure of investigated IL [Aliquat + ][Cl -].

Figure 1 .

 1 Figure 1. Hydrogen atom labeling and 1 H NMR (a), carbon atom labeling and 13 C NMR (b) in CDCl 3 . of ([Aliquat + ][Cl -]).

Figure 2 .

 2 Figure 2. Optimized structures of [Aliquat + ][Cl -] and its cation by using the B3LYP/6-31G* method.

Figure 3a .

 3a Figure 3a. Orientation and direction of dipole moment vector corresponding to cation of [Aliquat + ][Cl -] ionic liquid in gas phase by using the B3LYP/6-31G* level of theory.

Figure 3b .

 3b Figure 3b. Orientation and direction of dipole moment vector of [Aliquat + ][Cl -] ionic liquid in gas phase by using the B3LYP/6-31G* level of theory.

Figure 4 .

 4 Figure 4. Coordination modes of Cl atoms to cation in the [Aliquat + ][Cl -] IL.

Figure 5 .

 5 Figure 5. Molecular graphic for the [Aliquat + ][Cl -] IL in gas phase showing the geometry of all their bond critical points (BCPs), ring critical points (RCPs) and cage critical point (CCP) by using the B3LYP/6-31G* method.

Figure 6 :

 6 Figure 6: TGA and DTA curves of ([Aliquat + ][Cl -]) IL.

Figure 7 .

 7 Figure 7. Experimental Infrared spectra of [Aliquat + ] [Cl -] IL in solid phase compared with the predicted for the cation and IL in gas phase by using the hybrid B3LYP method.

Figure 8 .

 8 Figure 8. Experimental Raman spectra of [Aliquat + ] [Cl -] IL in solid phase compared with the predicted for the cation and IL in gas phase by using the hybrid B3LYP method.

Table 1 .

 1 Calculated

	uncorrected and corrected total energies (E), dipole moments (µ) and
	volumes (V) of [Aliquat + ][Cl -] and its cation in gas phase by using the B3LYP/6-31G*
	method.
		B3LYP/6-31G* Method
	Species	E	ZPVE	µ (D)	V (Å 3 )	ΔV
	[Aliquat + ][Cl -]	(Hartrees) -1500.1637	(Hartrees) -1499.3967	12.60	533.2	(Å 3 ) 39.3

  of those other interactions are observed in the [Aliquat + ][Cl -] IL in gas phase by using the B3LYP/6-31G* method[START_REF] Glendening | NBO 3.1[END_REF][START_REF] Bader | Atoms in Molecules, A Quantum Theory[END_REF][START_REF] Biegler-Köning | AIM2000; A Program to Analyze and Visualize Atoms in Molecules[END_REF]. Hence, the first analysis performed for the IL by using the NBO program shows only three interactions with higher energy values, which are the LP(4)Cl81*C5-H6, LP(4)Cl81*C30-H31 and LP(4)Cl81*C77-H78 interactions with values respectively of 23.78, 31.27 and 24.91 kJ/mol with a total energy value of 79.96 kJ/mol. Note that the second interaction is stronger than the other ones because the distance between H31 and Cl81 is 2.308 Å. All these interactions are performed from lone pairs of Cl atom to antibonding sigma C5-H6, C30-H31 and C77-H78 orbitals. Here, it is necessary to clarify that the cation of IL does not show interactions in both media, as was evidenced in the study of [Aliquat + ] [NTf 2 -

	of the C2-H46, C11-H47 and C2-H65 bonds, as supported by atomic MK charges and bond
	orders values of involved atoms. For these reasons, it is necessary to investigate the formation

of other intra-molecular or H bonds interactions in addition to those ionic bonds. Hence, the second order perturbation theory analyses of Fock matrix in NBO Basis by using the NBO program and the topological properties with the AIM 2000 program were used in order to predict if some

Table 2 .

 2 Observed and calculated wavenumbers (cm -1 ) and assignments for [Aliquat + ][Cl -] ionic liquid and its cation in gas phase by using the hybrid B3LYP Method.

	Experimental a			B3LYP/6-31G* Method
	IR	Raman		[Aliquat + ] b	[Aliquat + ][Cl -]
			SQM c	Assignments b	SQM c	Assignments a
			3081	aCH3(C77)	3060 aCH3(C77)
		3067sh	3068	aCH3(C77)	3026 aCH3(C77)
			3032	aCH2(C30)	3016 aCH2(C2)
		3029sh	3030	aCH2(C2)	3002 aCH2(C5)

Table 3 .

 3 Scaled internal force constants for [Aliquat + ][Cl -] and its cation in gas phase compared with reported for [BMIM][OTF] by using the B3LYP method and different basis sets. Units are mdyn Å -1 for stretching and mdyn Å rad -2 for angle deformations. a This work, b From Ref[START_REF] Assenine | Synthesis, thermal properties, vibrational spectra and computational studies of Trioctylmethylammonium bis (trifluoromethylsulfonyl) imide ionic liquid, Submitted to[END_REF],

		B3LYP method
	Force constants	6-31G* a	6-311++G**
		[Aliquat + ][Cl -] a	[Aliquat + ] b	[BMIM] c	[BMIM][OTF] c
	f(N-CH 3 )	3.86	3.95	4.40	5.06
	f(N-C 3 )	2.45	3.49
	f(CH 2 )	4.73	4.75	4.73	4.73
	f(CH 3 )	4.85	4.91	4.87	4.84
	f(CH 2 )	0.81	0.79	0.77	1.28
	f(CH 3 )	0.56	0.56	0.52	0.54

c

From Ref

[START_REF] Kausteklis | DFT study and vibrational assignment of 1-Butyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid by using the FT-Raman spectrum[END_REF]

for [BMIM][OTF].

ACKNOWLEDGEMENTS

This work was supported with grants from financial support by The Ministry of Higher Education and Scientific Research (MESRS) of Algeria in PRFU project code: B00L01UN200120180002 and, from CIUNT Project Nº 26/D608 (Consejo de Investigaciones, Universidad Nacional de Tucumán). The authors would like to thank Prof. Tom Sundius for his permission to use MOLVIB. Didier Villemin: Conceptualization; Project administration. Mostefa Boumediene: Conceptualization; Data curation. Mustapha Rahmouni: Conceptualization; Data curation. Serge Bresson: Methodology; Resources.

ρCH2(

Supplementary Information (SI).

Supplementary Information: Tables S1-S3 and Figures S1-S3.

DECLARATION OF INTEREST STATEMENT

Mohammed Amin Assenine: Methodology; Data curation.

CONFLICTS OF INTEREST

The authors declare no conflict of interest.


Pierre Thibault

Pantxo Diribarne

Thierry Fournier

Sylvain Perraud

Laurent Puech

P.-Etienne Wolf

Bernard Rousset

Roser Vallcorba

On the design of capacitive sensors using flexible electrodes for multipurpose measurements

This article evaluates the potential of capacitive measurements using flexible electrodes to access various physical quantities. These electrodes are made of a thin metallic film, typical thickness 0.2 m, evaporated on a plastic substrate. Their large flexibility enables them to be mounted in complex geometries such as curved surfaces. In the configuration of planar condensers, using a very sensitive commercial capacitive bridge and a three-terminal measurement method, several measurements are presented. A relative resolution of 10 -8 for the thermal expansion of samples is obtained at low temperature in a differential configuration. The same technique adopted for pressure gauge measurements at low temperature led to a typical 0.1 Pa resolution over a dynamic range of 10 4 Pa. In the configuration of interleaved electrodes, condensers have been used to measure wetting by either bulk liquid helium or by thin continuous helium films in a cylindrical pipe. Both experimental and numerical evidence is provided, showing that the close proximity of a reference ground potential significantly increases the relative sensitivity to fluid wetting. Further, interleaved electrodes can be used to access both the area that is covered by a liquid film but also to determine the thickness of this film, provided it is comparable to the periodicity of the electrode pattern.

I. INTRODUCTION

Capacitive sensors are widely used to measure various physical quantities. The review by Adams 1 points out the main characteristics and possible designs in the case of pressure gauge measurements. However, in many situations of interest, it proves to be difficult to build a system that fully obeys the law of a parallel plate condenser with a capacitance given by C = S ͑S / l͒, where S = R ϫ 0 , with 0 the dielectric constant in vacuum, R the relative permittivity of the medium separating the electrodes, S their common surface, and l the gap. To approach this limit, metallic electrodes deposited on a flexible plastic foil ͑like Kapton TM polyimide film͒ can be used, the plastic film being further glued on metallic supports attached to the measuring cell. If a guard ring is simultaneously evaporated, consisting of a metallic grounded region at a distance shorter than the length l surrounding the active electrode, a good approximation of a parallel plate condenser is experimentally realized. Such a design is described in Sec. II and successfully illustrated by thermal expansion measurements of samples of typical length L = 1 cm with a typical resolution ⌬L / L =10 -8 . In Sec. III, the same principle is applied to the construction of a pressure gauge for cryogenic use that is leaktight with a membrane on which the electrodes were glued. In Sec. IV, these techniques are generalized to liquid level measurements using interleaved electrodes. In this case, the dielectric constant and the thickness of the polyimide substrate come into play to determine the sensitivity. This issue is illustrated by a number of experiments and by numerical simulations, as this design may encounter a great deal of applications.

II. THERMAL EXPANSION MEASURING CELL

While designing a condenser for a specific use, a very pragmatic solution with moderate input consists of optimizing the ratio between the response to changes of the quantity of interest ͑let us say the length of a sample͒, to that due to the change of the environment, which should ideally be zero. In the situation of an ideal parallel plate condenser, considering two electrodes separated by a gap l Ϸ 0.1 mm, surface area S Ϸ 1 cm 2 , the capacitance in vacuum is only C Ϸ 8.85 pF. The measurement of this capacitance with a Sauty-type bridge would already give a decreased sensitivity due to the serial combination of the coaxial lead capacitance and that of the sample. Typically, with standard coaxial lines, this can be 100 pF per meter and the corresponding sensitivity is reduced by a decade or more. The use of capacitive bridges in the well-known three-terminal configuration as described in Ref. 1 is therefore advantageous, as it is not sensitive to the mutual capacitance between the electrodes and the ground. According to this principle, the sensors described in this paper obey four rules.

͑i͒

The two electrodes are electrically well-insulated from the ground, which also acts as an electrical shield. ͑ii͒

The electrodes are the major source of the signal. This is obtained by keeping the capacitance large compared to that of the connecting leads. ͑iii͒ The approximation of negligible finite-size effects is valid. The fact that the electrical field lines are not everywhere perpendicular to the surface of the electrodes is responsible for leakage of the field, which can be minimized if a grounded conductor ͑or guard ring͒ is placed around the electrode at a distance shorter than the gap. ͑iv͒ Whenever possible, a differential geometry is preferred in order to enhance the sensitivity.

These points are illustrated in the cell geometry of Fig. 1, which was used for thermal expansion measurements of silica-aerogels at low temperature, shown in Fig. 2. ͑See Ref.

2 for the context of this experiment.͒ The electrodes were drawn on single-face copper-coated Kapton, and the guard ring obtained by chemical etching of the copper using a photosensitive resin. After gluing with epoxy on the copper cell body, they form two parallel plate condensers. When the sample expands or contracts relatives to the copper cell, the gaps on both sides of the rotation axis, l X and l R , change in opposite directions from their initial values. The measurements were performed using a differential bridge commercialized by Barras-Provence. [START_REF]ABB Barras-Provence capacitive bridge[END_REF] While measuring the ratio between the unknown capacitance C X and the reference capacitance C R , the dielectric constant of the fluid does not appear in the quantity X -1 =1+C R / C X =1+l X / l R . Furthermore, this configuration ensures that the force exerted on the sample under measurement is small and constant, as the Archimedes forces on plates compensate each other. This point is of importance as these samples have an unusually low bulk modulus ͑a few bars͒ and must be measured free of stress. The best relative resolution achieved in this configuration was 10 -8 , corresponding to the nominal resolution of the bridge.

III. PRESSURE GAUGE

A pressure gauge has also been designed according to specifications ͑i͒ to ͑iv͒. The whole mechanical system ͑excluding the electrodes͒ is depicted in Fig. 3. It relies on a capacitive measurement of the deflection of a Cu-Be flexible membrane onto which the electrodes are glued. The membrane of thickness e = 0.15 m is rigidly held at the edges. The change in capacitance resulting from a deformation of the membrane is measured in a differential manner. Electrodes 1 cm in diameter are centered on the middle of the membrane and surrounded by a guard ring. The two halves of the copper cell are sealed onto either side of the Cu-Be membrane using Helicoflex aluminum seals. The cell is made leak-tight at a level of 10 -10 mbarϫ l/s.

A calibration at room temperature is given in Fig. 4. The sensibility is good over a large pressure range and the resolution excellent even over a reduced pressure range. For small deflections of the membrane, the deformation of the membrane relative to the gap l 0 is approximated by 4

z͑r͒ l 0 = ⌬p Y ͑R 2 -r 2 ͒ 2 l 0 e 3 3 16 ͑1 -2 ͒, ͑1͒
where ⌬p is the pressure difference, Y the Young modulus, R the membrane radius, r the electrode's radius, e the thickness of the membrane, and the Poisson ratio. For larger deflections, the deflection of the membrane is not uniform, and depends on the radial position. Rewriting Eq. ͑1͒ in dimensionless form z͑r͒ / l 0 = ͑R 2r 2 ͒ 2 / a͑p͒ 4 , an integration leads for each condenser to

C LP = -0 R LP a 2 l 0 1 2 Ά ln 1 + R 2 -r 2 a 2 1 - R 2 -r 2 a 2 -ln 1 + R 2 a 2 1 - R 2 a 2 · , ͑2͒ C HP = -0 R HP a 2 l 0 ͭ arctanͩ R 2 -r 2 a 2 ͪ-arct anͩ R 2 a 2 ͪͮ.

͑3͒

The dotted lines in Fig. 4 correspond to Eqs. ͑2͒ and ͑3͒, using Y = 80 GPa, e = 150 m, and = 0.3. For small deflections and for symmetric initial gaps, the capacitance ratio is determined from X -1 =1+͑ R LP / R HP ͒͑1+2z / l 0 ͒, corresponding to the sensitivity ͑⌬X / X͒ / ⌬p = -1.5ϫ 10 -5 / Pa. For the largest deflections, experiments show that a further correction is necessary, involving an increase of the rigidity due to larger strains on the membrane. However, thanks to a good reproducibility of the results, these data are used as calibration values. Note that a remarkably low level of noise is obtained from the use of a rather rigid membrane associated with a precision capacitance bridge, with a typical resolution better than 0.1 Pa.

This pressure gauge was employed in cryogenic conditions to measure a superfluid helium mass flow rate in a Venturi device. The main difference from the room temperature calibration was an unexplained enhanced threefold sensitivity.

IV. PERIMETER THAT IS WETTED BY A FLUID

A. Objective

Many situations require the measurement of liquid levels in both a precise and nonintrusive manner. Capacitive methods use the contrast in dielectric constant between the two phases. This contrast may result from a difference in density of the two phases of a pure body ͑a liquid and its vapor for instance͒ or a combination of both the polarizabilities and the densities ͑a liquid in contact with a gas, two liquid phases of different species͒. A common configuration for capacitive measurements is the case when the two electrodes constituting the condenser are perfectly coupled. This is achieved with coaxial condensers or parallel plate condensers, with the drawback that the distance between the electrodes is generally less than 1 mm. The reasons for these choices are to obtain large enough capacitances ͑picofarad or more͒ and negligible edge effects. For a fluid, the presence of these two closely spaced electrodes may affect its motion ͑moving fluid͒ and give rise to unwanted phenomena such as capillary rise.

A geometry of interleaved electrodes deposited on an insulating material, being nonintrusive, has been used by several authors. A version of this system has been patented by Bosch 5 to measure a fuel film in the intake duct of an internal combustion engine. In that case, several small discrete condensers were used to get information on the film presence at different locations. The Kapton film was glued on a grounded support, and the measurements were performed using a three-terminal method. The patent claim was that this geometry was particularly suitable to screen spurious effects due to electrical coupling, and also to enhance the sensitivity to wetting by the fluid.

This work came to our attention after observing that, while measuring the wetting by a liquid helium film in a pipe with a similar technique, the response was surprisingly high and reproducible. The reasons for this interest in cryogenic superfluid two-phase flow in a horizontal pipe is discussed in Refs. 6 and 7. The results observed under cryogenic conditions with superfluid helium are not specific to this fluid, and its particularly low dielectric constant ͑1.056 at saturating vapor pressure and 1.8 K͒ nicely illustrates the high sensitivity that can be obtained with this method.

B. Designing the sensors

For a continuous liquid level detection, the electrodes forming the planar condenser are evaporated on a flexible plastic film in an interleaved geometry shown in Fig. 5. With t the thickness of the Kapton polyimide, w the width of the electrodes, and g the gap between electrodes, the periodicity of the structure is =2͑w + g͒. For a typical arrangement on a rectangular 15ϫ 30 mm geometry using t =50 m, w = 200 m, and g = 100 m, the total length of pairs of opposite electrodes is L = 1.5 m. Figure 5 illustrates this arrangement.

Much effort was devoted to obtaining a metallic layer which is firmly bound to the substrate. After careful cleaning of the Kapton film with reactive ion etching, good adhesion was achieved by the successive evaporation of a 10 nm thick Ti layer followed by a 200 nm thick layer of gold. The interleaved pattern is obtained either using a negative resin with directional evaporation on the Kapton, or a positive resin and chemical etching of the gold on a preplated sample. The condenser is eventually glued with epoxy on a metallic substrate in the desired experimental arrangement.

Figure 6 illustrates the case where the condensers were designed to fit inside the inner perimeter of a 40 mm stainless-steel pipe. A thin metallic Cu-Be ring supports four condensers glued on its inner circumference. A Teflon cylinder was used to apply pressure on the condensers during the gluing process. The Cu-Be ring is then inserted in the pipe and the electrodes are electrically connected using Cu wires and silver paint. This geometry was used to measure liquid levels in stratified two-phase flows of helium without perturbation. 8

C. Calibrating the sensors

A major improvement of the system as compared to that patented by Bosch is that the sensitivity to the fluid is tunable by a proper choice of the geometry. The claim of the patent is that, "The capacitive sensor according to the invention has the advantage that the relative capacitance change on wetting the electrodes is large, since the additional ground electrode reduces the capacitive coupling between the electrodes by the rear side of the sensor, so that the largest capacitive contribution is supplied by the space between the electrodes on the one or top sensor side. Furthermore, the ground coating on the sensor rear side ͑or side remote from the side the electrodes are on͒ acts as a shield, so that the influence of interfering electrical fields is neutralized and the grounding surfaces in the vicinity of the rear side of the sensor do not influence the characteristic properties of the sensor." [START_REF] Magenau | for Bosh GmbH[END_REF] However, many situations require a quantitative knowledge of the sensor response to a given change in the fluid dielectric constant, and this point was not addressed.

To achieve this goal, the response of several interleaved condensers was measured after immersion in fluid of various dielectric constants. The high-precision bridge used for the measurements is commercialized by Andeen-Hagerling [START_REF] Model | [END_REF] and works in a differential configuration using a built-in reference capacitor. Experimentally, the measured capacitances are compatible with a simple model of two capacitances in parallel given by Eq. ͑4͒,

C measured = C ins + C fluid .
͑4͒

The physical interpretation of C ins is therefore the capacitance associated with the field in the insulated side ͑Kapton plus glue, interrupted by the plane at zero potential͒, and C fluid is the capacitance of the half-space occupied by the fluid phase. If C vacuum represents the capacitance in vacuum, C fluid is given by Eq. ͑5͒, and a sensitivity factor f is defined from Eq. ͑6͒, that corresponds to the field lines that are affected by the presence of the fluid,

C fluid = R fluid ϫ C vacuum , ͑5͒ f = C vacuum C ins + C vacuum . ͑6͒
A general expression is obtained with Eq. ͑7͒ that is valid for both the gas and the liquid phase, and that contains the factor f, which is a characteristic of the condenser,

C bridge = C vacuum ͑1 + f͑ R fluid -1͒͒. ͑7͒
It was found that, for several condensers having the same period and same substrate thickness, and with several fluids at different temperature and for different dielectric constants ͑air ͓ R Ϸ 1͔, toluene ͓ R = 2.38͔, liquid nitrogen ͓ R = 1.44͔, svp helium at 4.2 K ͓ R liq = 1.049, R vap = 1.005͔, svp superfluid helium at 1.8 K ͓ R liq = 1.0573, R vap = 1.0002͔͒, that the sensitivity factor f was constant at 0.70± 0.03. This observation suggests that the observed dispersion is due to the nonreproducible process of gluing. It is remarkable that the absolute value of C vacuum may change by 10% or more, when for instance some of the teeth of the comb are missing, but this has no consequence on the dynamics of the measurements as defined by the factor f.

D. Linear behavior of the liquid level sensors

The response of the capacitive sensors as a function of the wetted fraction has been tested in several configurations. Figure 7 shows the capacitance of a vertical rectangular sensor as a function of the immersed depth in toluene. The behavior is linear as expected, and the slope follows Eq. ͑7͒. In this experiment, the liquid level is fixed, and the sensor progressively immersed in the liquid. The absolute physical origin is not known, as the response starts with the rise of the meniscus of the fluid on the sensor. No prewetting occurs under these conditions, but the dewetting is partially hysteretic, and was not systematically investigated.

Another test was performed in superfluid liquid helium at saturated vapor pressure and 2 K in an optical cryostat with the capacitor configuration shown in Fig. 6. In the experiment, the responses of four capacitive sectors are re-corded as the liquid level decreases due to evaporation. The liquid height h is measured optically from the bottom of the cylinder of radius R, and Fig. 8 represents the response of the sensor having its end at the top of the cylinder, and its bottom near the midheight of the cylinder. The plot represents the change in capacitance as a function of the quadrant perimeter given by R /2ϫ arccos͓1͑-h / R͔͒. The total change in capacitance agrees with previous calibrations, but dewetting is delayed due to the presence of the meniscus. This corresponds to the jump observed on the figure at high liquid level. At midheight of the cylinder, the wall is perpendicular to the liquid-free surface, and the meniscus height given by ͱ 2 C , where C is Laplace's length ͑ C = 0.46 mm for helium at 1.8 K͒.

E. Thickness of a liquid film

An analytic 2D solution is known for a structure which is symmetric with respect to the plane of the electrodes, which are of negligible thickness. [START_REF] Landau | Course in Theoretical Physics VIII, Electrodynamics of Continuous Media ͑Pergamon[END_REF] In a semi-infinite comblike structure, the electric field must be evanescent in a direction z perpendicular to the plane of the electrodes. Defining a wave vector k 0 =2 / , with the periodicity of the potential, one shows that the electric field is localized in the vicinity of the structure, over a typical distance given by /4. This result was used in Ref. 11 to measure the thickness and to manipulate thin films of helium on a silicon substrate with an interleaved structure with a gap size of some micrometers. Note that in the present case, the size of the gap being 100 m instead of 5 m in their study, the electrical field near the structure is 20 times less and the electrostatic forces 400 times less for the same polarization of the electrodes ͑typically 8 V͒.

In order to extend these exact results to the film thickness dependence of interleaved electrodes on Kapton, the problem was solved numerically using the electrostatic finite element module of the ANSYS software. The boundary conditions are defined by the exact geometry of the electrodes, and the electric field normal to the electrodes computed from the charges. An additional insulating layer between the

043903-5

Flexible capacitive sensors Rev. Sci. Instrum. 78, 043903 ͑2007͒ 50 m thick Kapton foil and the ground was considered, corresponding to the epoxy glue. For simplicity, a total thickness of plastic t =70 m ͑Kapton plus glue͒ is used, and the dielectric constant is adjusted to mimic the experimental data. An example of equipotential lines is shown in Fig. 9 in a typical configuration corresponding to wetting by a thin helium film. In this case, the dielectric constant is so close to 1 that the equipotential lines are hardly affected by the fluid presence.

The response of a sensor as a function of the film thickness is given in Fig. 10. The insert on the graph represents the same data on a semilog plot, according to Eq. ͑8͒. The capacitance C L fl , corresponding to a film of thickness L fl , is normalized relative to C ϱ corresponding to very thick films and to C 0 with no liquid on the electrodes,

C ϱ -C L fl ϰ exp -2k 0 L fl . ͑8͒
The slope -0.021 ͑in m -1 ͒ resulting from the numerical simulation compares favorably with an evanescent field decaying over the typical length /4 =48 m. A more careful analysis with high-order terms for the potential shows that the sensitivity is enhanced for small films, and tends to an exponential law for thick films.

F. Discussion

As expected, an interleaved structure covered by a liquid film of small dielectric constant in the presence of a grounded plane on the opposite side reproduces the proper-ties of the evanescent electric field. This result has been obtained from a comparison with the analytic solution of the 2D symmetrical geometry, and relies on the periodicity of the potential.

However, a direct comparison for the total capacitance obtained from the analytic solution of the 2D geometry and that measured experimentally is notably different. Denoting K the complete elliptic integral of first kind and KЈ the complementary function, one expects a capacitance per unit length and per pair of electrodes, given by Eq. ͑9͒, A simple scheme is proposed to understand the high sensitivity of these sensors when modeled into two separate half-spaces. The value of the capacitance C ins is minimal, despite a large dielectric constant ͑ R = 3.4͒, because its thickness is less than /4. For the open half-space, the total capacitance is reduced due to the proximity of a grounded plane, but its dynamics is given by the fluid dielectric constant.

C = 2 0 Kͩsin k 0 a 2 ͪ KЈͩsin k 0 a 2 ͪ . ͑9͒ Using
A more systematic electrostatic study of the influence of the geometric parameters has also been performed and will be published elsewhere. [START_REF] Thibault | [END_REF] It shows that the sensitivity of planar condensers in the adopted geometry is comparable to that of a condenser with perfectly coupled electrodes, but with a reduced capacitance. We obtained for instance on 50m thick Kapton substrates experimental sensitivity factors that are, respectively, f = 0.36, 0.43, 0.70 in the case of interleaved electrodes presenting gaps g of 30, 50, or 100 m and for electrode widths w =2g.

For practical purposes, in a single experiment, one cannot distinguish between the partial wetting of a sensor by bulk liquid, or by a continuous thin film. Figure 11 illustrates this result in a fictive situation. It shows that a sensor response of 68% can be obtained in two different ways. Assuming the film is continuous, it corresponds to a 15 m thick film ͑structure with a gap of 30 m͒ or to a 25 m thick film ͑structure with a gap of 50 m͒. Assuming the film is thick with respect to both characteristic lengths, we would deduce that the surface that is wetted by the fluid is 68% of the total sensor surface on both structure. A combination of sensors of different gap size may thus be used ͑see Ref. 13, for instance͒ to distinguish between theses two cases, as the responses are thickness but also coverage dependent.

V. CONCLUSION

Many devices working on the principle of capacitive detection using flexible electrodes are discussed in this article. The examples that are given are not exclusive, but cover a number of possible applications. For each use, particular at-tention has to be devoted to the most suitable design to reach the desired sensitivity. For many realizations, minimal effort is required, particularly when the electrodes do not need micron-size resolution. In this case, standard tools for electronic circuitry design are sufficient. Some applications may not require capacitive bridges as accurate and expensive as those cited in this article as long as they include a threeterminal measurement configuration. In particular, we recently obtained good results using the two-channels capacitive-to-digital AD7746 Analog Devices 14 converter associated with its evaluation board. It allows both differential and absolute capacitive measurements with a typical femtofarad resolution, with a ±4 pF dynamic range for a condenser with initial capacitance value between 0 and 17 pF. For this reason, we have designed capacitors corresponding to this dynamic range, and obtained accurate liquid level measurements. The system being very affordable, we plan to generalize its use to other contexts.

FIG. 1 .FIG. 2 .

 12 FIG.1. Side view of a dilatometer based on a differential capacitive detection. Sample expansion is measured respective to that of the copper cell body. A common electrode is glued on the central moving part. Small copper pins serve for the axis of rotation, without significant friction.

FIG. 3 .

 3 FIG. 3. Left: Expanded view of the pressure cell. ͑1͒ Fill line and electrical connections. ͑2͒ and ͑5͒ Support for the soft electrodes. ͑3͒ Helicoflex aluminum ring. ͑4͒ Cu-Be membrane.

FIG. 5 .

 5 FIG. 5. Left: Photograph of a planar condenser with gold electrodes evaporated on a Kapton film. The two interleaved combs are separated by a 100 m wide gap. Each comb is constituted of 50 teeth. Right: Schematic illustration of the arrangement used for liquid level measurements ͑in the absence of meniscus͒.

FIG. 7 .

 7 FIG. 7. Test of the linear response of a capacitive sensor progressively immersed in liquid toluene.

  the geometric parameters w = 200 m, g = 100 m, and the developed length of L = 1.5 m of paired electrodes gives 34 or 17 pF per half-space. This is more than twice what is measured for the contribution on the side of the fluid, given by C vacuum = f ϫ C empty Ϸ 7.7 pF. The grounded plane thus decreases the absolute capacitance of the open space.

FIG. 9 .FIG. 10 .

 910 FIG. 9. Example of equipotential lines close to the electrodes for an interleaved structure of gold electrodes on Kapton. The liquid is helium, of relative dielectric constant R liq = 1.057 at 1.8 K.

Downloaded 17 Jun 2013 to 193.48.255.141. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissions

Rev. Sci. Instrum. 78, 043903 ͑2007͒ Downloaded 17 Jun 2013 to 193.48.255.141. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissions

ACKNOWLEDGMENTS

The authors are grateful to C. Lemonias, B. Fernandez, and T. Crozes, for their invaluable help in the realization of the samples, J.-L. Bret for improving the measurements, and C. Guttin for drawing our attention to the performances of the Analog Devices capacitive to numeric converter. The authors would also like to thank J. Butterworth from Air Liquide Co. for his help in preparing this article.