Rinaldo Poli

Christine Bibal
email: christine.bibal@iut-tlse3.fr

Jean-Claude Daran

Simon Deroover

Ionic Schiff base dioxidomolybdenum

Keywords:

come

Introduction

The use of two-phase solvent systems, especially those based on water-soluble ligands and their metal complexes [1], has emerged in the last decade as a synthetic strategy for homogeneous catalysis. In this respect, room temperature Ionic Liquids (ILs) as solvents have proved to be mainly useful for these types of two-phase catalytic reactions [2]. Particularly, the interest in ILs as alternatives to organic solvents has been growing with regards to economic and ecological concerns [3]. However, ILs have only recently been applied to metal transition catalysis [4] with the benefit of a convenient catalyst separation, hence, recovery/recycling procedure. Catalyzed oxidations in ILs have resulted in a few processes that are more efficient than those carried out in organic solvents [5]. The efficiency of the catalyst/ILs system is strongly dependent on the nature of the ILs. The rationalization of its role in association with the catalyst remains an unexplored research area. Nevertheless, Dupont et al have already shown the "non-innocent" nature of ILs under certain reaction conditions [6].

In oxidation catalysis, the choice of a suitable ligand is often delicate because it must also be resistant towards the oxidant. The most efficient Jacobsen's and Katsuki's catalysts have evolved as standard reagents for asymmetric epoxidation reactions due to the ease of the Schiff base synthetic generation [7]. It was found that in some cases the activity of both catalysts was increased by adding ionic liquids to the reaction mixture [8]. However, decreasing yields were obtained during successive runs due to either catalyst decomposition under basic conditions or loss of material in the work up process. As a result, a better immobilized catalyst in the IL phase with the adequate ionic structure would permit developing a convenient experimental procedure for a suitable biphasic reusable catalytic system.

Among different families of metal complexes used as oxidation catalysts, complexes of the type Mo(VI)O2L have received special attention [9]. With the coordinating ligand L functioning as a mono-, bi-, tri-, or tetradentate ligand, these molecular constructs have already been shown to be effective catalysts or catalyst precursors for olefin epoxidation.

Representative members of that kind possess the following general formula: [MoO2X2(L 1 )n],

[MoO2X(L 2 )(L 1 )n] and [MoO2(L 2 )2(L 1 )n] (X = Cl, Br, CH3, OR etc; L = mono or bidentate neutral (L 1 ) or anionic (L 2 ) ligands with nitrogen, oxygen/sulfur donors) [10]. Related versions with multidentate dianionic ligands are also used. Specifically, dioxidomolybdenum(VI) complexes bearing tetradentate dianionic salen ligands are promising reagents for this type of chemical transformation reaction [11]. Complexes containing tridentate dianionic Schiff base ligands of the type MoO2(L)(D) (D = solvent) possess a labile ligand D suitable for substrate activation and oxidant uptake [12]. However, the use of dioxidomolybdenum(VI) complexes in combination with ILs is limited and has only been described rarely in literature to date [13].

One synthetic strategy to gain an enhanced solubility of the catalyst in ILs may be accomplished by introducing ionic functionalities on the ligand periphery. Synthetically modified MoO2(L) complexes bearing anionic sulfonato (-SO3 -) functionalities may yield novel candidates for olefin epoxidation. Such compounds would not only be able to activate chemical bonds but also allow for reactivity in polar media with the additional benefit to performing catalytic applications in green media such as ILs and water, the latter probably being the most environment-friendly medium.

It is generally accepted that the Lewis acidity of dioxidomolybdenum(VI) complexes is one of the most important characteristics that determine catalytic performance in olefin epoxidation [14]. High turnover frequencies are often associated with a low electron density at the metal centre. Therefore, introducing an electron-withdrawing functionality such as sulfonate anions onto the salicylidene ring of the complex may hold potential for a better efficiency of the catalyst. Herein, we present the synthesis and the characterization of dioxidomolybdenum(VI) complexes with sulfonated tridentate Schiff base ligands. These complexes of the type MoO2L, L being a tridentate trianionic Schiff base ligand [sulfonated N-salicylidene-2-aminophenolate (sSAP 3-) or N-salicylidene-2-aminoethanolate (sSAE 3-)],

have been characterized by standard spectroscopic methods. These ligands are sulfonated versions of well known SAE 2-and SAP 2-Schiff bases [15].

Preliminary results for cyclooctene epoxidation in an aqueous medium and in different

ILs (ie [BMIM][NTf2] (NTf2 -= (CF3SO2)2N -), [BMIM][CF3SO3], [EMIM][CH3C6H4SO3])
with t-butyl-hydroperoxide (TBHP) as oxidant will be presented.

Experimental

Materials and methods

All

Preparation of Schiff base ligand NaH2sSAP, 1

Sodium salicylaldehyde-5-sulfonate (1,3 g, 5,80 mmol) and 2-aminophenol (0,63 g, 5,80 mmol) were combined in 30 ml of water/ethanol (1:1) and refluxed for 4h at 60°C. The yellow precipitate was filtered, washed with diethyl ether and dried in air to afford 1.24 g of the ligand 1. Yield: 68%. 1 H NMR (DMSO-d6,  (ppm)):6.84-7.87 (m, 7H, H aryl); 9.01 (s, 1H, CH=N); 9.78 (s, 1H, OH); 14.06 (s, 1H, OH). 13 C NMR (DMSO-d6,  (ppm)): 116. 04, 116.54, 118.03, 119.52, 119.65, 128.18, 129.56, 130.45, 134.56, 139.20 (C aryl); 151.17 FAB-MS: negative mode (M = 292, A -), (M = 607, [2 A -+ Na + ] -).

Preparation of Schiff base ligand NaH2sSAE, 2

Sodium salicylaldehyde-5-sulfonate (1,07 g, 4,77 mmol) and amino-ethanol (0,29 mL, 4,77 mmol) were combined in 20 ml of water/ethanol (1:1) and refluxed for 4h at 60°C. The crude solid obtained after evaporation of the solvents was recrystallized from absolute ethanol. Yield: 39%. 1 H NMR (DMSO-d6,  (ppm)): 3.64 (m, 4H, CH2) ; 4.81 (s, 1H, OH); 6.76 (d, 3 J HH = 8.6 Hz, 1H, H aryl) ; 7.52 (d, 3 J HH = 8.6 Hz, 1H, H aryl) ; 7.66 (s, 1H, H aryl); 8.54 (s, 1H, CH=N); 13.86 (s, 1H, OH). 13 C NMR (DMSO-d6,  (ppm)): 60.35,60.54 (CH2);116.06,116.91,128.90,129.99,138.59 (C aryl); 162.05 (C-O); 166.61 (CH=N). Selected IR bands (KBr, cm -1 ): 3488(br), 3395(br) ν(OH); 2947(m), 2922(m), 2889(m) ν(C-H); 1659(s) ν(C=N), 1610(s); 1518(s), 1450(s), 1407(m), 1385(m), 1361(m), 1324(m), 1294(m), 1220(s); 1188(s); 1172(s), 1112(s), 1082(m), 1038(s) ν(SO3 -). FAB-MS: negative mode (M = 244, A -), (M = 511, [2A -+ Na + ] -), (M = 778, [3A -+ 2Na + ] -).

Synthesis of complex MoO2(sSAP)Na, 3

A solution of 1 (480 mg, 1.52 mmol) and MoO2(acac)2 (497 mg, 1.52 mmol) in absolute ethanol (35 mL) was refluxed for 2h. The obtained orange precipitate was then filtered and dried in air. Yield: 55%. 1 H NMR (DMSO-d6,  (ppm)): 6.82-8.09 (m, 7H, H aryl); 9.36 (s, 1H, CH=N). 13 C NMR (DMSO-d6,  (ppm)): 116.77, 117.32, 118.41, 120.60, 120.90, 130.21, 132.36, 132.97, 135.73, 141.

Synthesis of complex MoO2(sSAE)Na, 4

The same procedure that was applied to yield complex MoO 2 (sSAP)Na 3 was used for the synthesis of the analogue complex 4. Yield: 71%. 1 H NMR (DMSO-d6,  (ppm)): 4.01 (m, 2H, CH2); 4.41 (m, 2H, CH2); 6.82 (d, 3 J HH = 8.5 Hz, 1H, H aryl); 7.66 (dd, 3 J HH = 8.5 Hz,  (ppm)): 60.95 (CH2-N), 71.59 (CH2-O); 118.72,119.52,130.97,132.14,139.68 (C aryl);164.11 (CH=N). Selected IR bands (KBr, cm -1 ): 3450(br) ν(OH); 2953(m), 2927(m), 2867(m) ν(C-H); 1640(s) ν(C=N), 1605(m); 1549(m), 1468(m), 1373(m), 1301(m), 1207(m); 1170(m), 1118(s), 1043(s), 1036(s) ν(SO3 -) ; 936(m), 911(s) ν(Mo=O), 896(sh). FAB-MS: negative mode (M = 372, A -).

Synthesis of complex MoO2(sSAP)NBu4, 5

Tetrabutylammonium bromide (74 mg, 0,23 mmol) was added in small portions to complex 3 (105 mg, 0.20 mmol) which was solubilized in 1 ml of water. The orange precipitate that appeared immediately after addition was filtered. Yield: 68%. 1 H NMR (DMSO-d6,  (ppm)): 0.92 (t, 3 J HH = 7 Hz, 12H, CH3); 1.29 (q, 3 J HH = 7 Hz, 8H, CH2) ; 1.55 (m, 8H, CH2) ; 3.15 (m, 8H, NCH2) ; 6.81-8.09 (m, 7H, H aryl); 9.35 (s, 1H, CH=N). 13 C NMR (DMSO-d6,  (ppm)): 13.59, 19.29, 23.13, 57.57, 116.73, 117.29, 118.33, 120.55, 120.84, 130.14, 132.31, 132.94, 135.71, 141.28

Catalytic epoxidation of cyclooctene by complexes 3-5 in IL media

The catalytic reactions were performed in air in a reaction flask, equipped with a magnetic stirrer and immersed into a thermostated bath. A mixture of catalyst (70 mol, 0.01 eq), cyclooctene (0.80 g, 7.3 mmol, 1 eq), dodecane as internal standard (0.75 g, 1 mL) with 0.5 ml of ionic liquid equilibrated in air was stirred for 15 min at 55°C. At this temperature, anhydrous t-butyl hydroperoxide (5.5 M in n-decane, 2.1 eq, 15.4 mmol, 2.8 ml) was added (start of the reaction). Aliquots of the reaction medium were withdrawn at certain time intervals to monitor the reaction by quantitative GC analysis. The samples were treated with MnO2 to remove peroxides and diluted with 1 ml of diethyl ether. The resulting slurry was filtered on silica gel, eluted with 10 ml of diethyl ether and the filtrate was injected in the GC.

The conversion of cyclooctene, and the formation of cyclooctene oxide were calculated according to calibration curves (r 2 = 0.999).

Catalytic epoxidation of cyclooctene by complex 3 with TBHP (70% in water)

The same procedure as for the epoxidation in IL media was employed with the following quantities of reactants: catalyst 3 (65 mg, 0.127 mmol, 0.007 eq), cyclooctene (2.6 mL, 18.8 mmol, 1 eq), TBHP (70% in water, 10 mL, 74.4 mmol, 4 eq) and dodecane (150 mg) as internal standard. The temperature in this experiment was adjusted to 80°C.

General procedure for the recycling of the catalyst 3 in [BMIM][NTf2]

The epoxidation was performed under the same reaction conditions as described in paragraph 2.7 for catalyst 3 (70 mol, 0.01 eq) in cyclooctene (0.82 g, 1 eq), dodecane (0.83 g), 0.5 ml of [BMIM][NTf2] and t-butyl hydroperoxide (5.5 M in n-decane, 2.8 ml). The upper organic phase was separated and the IL phase was extracted with pentane (4*5 mL).

The collected organic layers were assembled and injected into the GC to evaluate the residual cyclooctene fraction and the cyclooctene oxide yield. The IL phase was then dried under vacuum for 1.5 h to remove traces of pentane and t-BuOH formed in the catalytic run. The IL phase was reused in the consecutive cycle with a new charge of cycloooctene, dodecane and TBHP as it was in the first cycle. The same extraction procedure was re-applied for each consecutive cycle.

X-ray crystallography

A single crystal of each compound was mounted under inert perfluoropolyether at the tip of a glass fibre and cooled in the cryostream of either an Oxford-Diffraction XCALIBUR or a Bruker APEXII CCD diffractometer. Data were collected using the monochromatic MoK radiation (= 0.71073). The structures were solved by direct methods (SIR97) [START_REF] Altomare | SIR97-a program for automatic solution of crystal structures by direct methods[END_REF] and refined by least-squares procedures on F 2 using SHELXL-97 [START_REF] Sheldrick | Program for crystal structure refinement[END_REF]. All H atoms attached to carbon were introduced in idealised positions and treated as riding on their parent atoms in the calculations. In the ligand structure the H atoms attached to nitrogen and oxygen atoms were located in difference Fourier synthesis. For Molecule 2 (atoms O24 and N25), the H atom was clearly identified as bonded to atom N25 with no significant electron density on atom O24. For Molecule 1, on the other hand, two smaller electron densities were located near the atoms O14 and N15, indicating the coexistence of both expected tautomers. The two H atoms had equivalent peak height in the difference Fourier map and they were therefore introduced with occupancy factors of 0.50 each, which were not refined. These atoms were treated as riding on their parent atoms. In compound 3, the H atoms attached to water molecules were located in difference Fourier syntheses and their coordinates were initially refined using O-H [0.82(1) Å] and H•••H [1.39(2) Å] restraints. In the last stage of refinement, they were treated as riding with U iso = 1.5U eq (O). The drawing of the molecules was realised with the help of ORTEP3 [START_REF] Farrugia | ORTEP-3 for Windows[END_REF]. Crystal data and refinement parameters are shown in Table 1.

Results and discussion

Synthesis of sulfonated tridentate Schiff base ligands and the corresponding ionic

MoO2(L) complexes

The preparation of mono and di-sulfonated tridentate "ONO" salicylaldimine ligands has already been described in literature by Evans and Chakravorty [20]. Surprisingly, little is known for these molecules with respect to detailed characterization data such as X-ray structures, NMR and mass spectroscopy. Herein we will present the preparation of sulfonated Schiff base ligands NaH2L, L being N-salicylidene-2-aminophenolate sulfonate (sSAP 3-), 1,

or N-salicylidene-2-aminoethanolate sulfonate (sSAE 3-), 2, and their complexation onto the molybdenum metal, resulting in complexes 3 and 4 respectively, see Scheme 1. For the cis-dioxidomolydenum(VI) complex 3, the filtered orange precipitate turns reddish upon drying in air. Single crystals were obtained by slow solvent evaporation of a concentrated ethanol solution left at room temperature. The nature of the donor molecule for the NaMoO2LD structure in the solid state could be determined by performing a single crystal X-ray diffraction study. The structure reveals that the sixth coordination site of molybdenum is completed by a sulfonato oxygen atom from an adjacent molecule, indicated as D in Scheme 3 (see X-ray diffraction analysis section).

A cation exchange reaction was performed in the case of the dioxidomolybdenum complex 3 bearing the N-salicylidene-2-aminophenolate sulfonato ligand (scheme 4). The solubility of 3 in water and its good stability against hydrolysis of the -CH=N functionality allowed the reaction to occur in this medium at room temperature. The resulting ammonium complex 5 precipitated from the reaction medium and filtration allowed isolation of the compound in good purity. Crystals grown from a concentrated solution of 5 in ethanol were shown by single crystal X-ray diffraction to be composed of the desired salt with a noninteracting ammonium cation. Like in the structure of the analogue sodium salt 3, the coordination sphere around the molybdenum atom in the solid state is completed by a sulfonato oxygen atom from an adjacent molecule (see X-ray diffraction analysis section). Scheme 4. Cation metathesis of sodium salt 3 with ammonium bromide affording the ammonium dioxidomolybdenum complex 5.

Spectral features

In the 1 H NMR spectra of the Schiff base ligands NaH2L 1 and 2, the phenol OH proton resonances in para position to the sulfonato functionality are shifted downfield with respect to classic phenol proton signals. The OH signals disappear in the 1 H NMR spectra of the complexes indicating the effective binding of the ligand through a dianionic "ONO" tridentate mode. Furthermore, the singlet of the imine carbon proton shifts downfield compared to the corresponding signal in the free ligands through coordination of the nitrogen onto the molybdenum cation. It is also worth mentioning that in the 1 H NMR of the sSAE dioxidomolybdenum complex 4, the ethylene resonance is resolved into two distinguishable triplet signals in comparison to the corresponding single multiplet signal in the sulfonated NaH2sSAE ligand. No ethanol molecule (used as solvent in the synthesis) was observed as D ligand (Scheme 1) in the 1 H NMR spectra of 3 and 4 in DMSO-d6 and D2O. This is in contrast with the described structures of the corresponding neutral MoO2LD complexes (with L = SAP or SAE) obtained by the same experimental procedure [15]. These neutral complexes feature ethanol as D ligand and their 1 H NMR spectra display signals corresponding to the bonded and free D molecule (D = EtOH, H2O, DMSO) in fast exchange [15].

By IR spectroscopy, the presence of the sulfonato groups for both ligands and complexes is confirmed by three stretching frequencies in the range 1000-1200 cm -1 [21]. The Schiff-base structure for the salicylidene part of compounds 1-4 is confirmed by the strong characteristic imine band occurring in the range 1617-1659 cm -1 . Coordination of the imine centre onto the molybdenum atom results in a slightly lower (C=N) stretching frequency for the complexes 3 and 4 (1617 and 1640 cm -1 respectively) than for the free Schiff bases 1 and 2 (1621 and 1659 cm -1 respectively). In addition, two IR absorptions observed for 3 and 4, attributable to asymmetric and symmetric Mo=O stretches of the cis-MoO2 2+ moiety (in the range 900-930), are typical of MoO2LD structures.

Compounds 1-4 have also been identified by FAB spectrometry in the negative mode, showing the anion mass with the correct isotopic distribution. For ligands 1 and 2, aggregates are observed with the sodium cation. The FAB spectrometric analysis of the ammonium complex 5 showed the anion in the negative mode and the corresponding NBu4 + cation in the positive mode.

X-ray diffraction analysis for complexes 3 and 5

The molecular structures of 3 and 5 with the atom numbering shown in Figure 1 and Figure 2 are typical examples of cis-MoO2 complexes. The anionic molybdenum complex displays the same coordination geometry in the two salts, corresponding to a distorted octahedron where the sulfonato group of the adjacent complex occupies the sixth coordination site. The tridentate Schiff base ligand binds the molybdenum atom in a mer coordination mode through the N(1), O(1) and O(2) anionic oxygen atoms. The weaker -donors (the nitrogen atom and the oxygen atom of the sulfonate group) are trans to one oxido ligand. The relative arrangement of the adjacent molecules is the same in the two structures, with a mutual head-tail arrangement of two anions to generate pseudo-dimers. The sodium cation in 3 (see Figure 1) also features pseudo-octahedral coordination with two cis positions occupied by the sulfonate O( 5) atom and the O(4) atom from the Mo=O function located trans to the sSAP N atom. The remaining four coordination positions are occupied by water molecules, two of which bridge the sodium atom with a symmetry equivalent (inversion center) sodium atom, generating an infinite network which includes H-bonds (a table of H-bonding parameters is available in the Supporting Information). In the structure of 5, on the other hand, the ammonium cations do not establish any close contact with the anionic part, which is therefore featured by discrete and isolated pseudo-dimers (Figure 2).

X-ray crystallographic analysis of [HOCH2CH2NH3][H2sSAE]

Slow solvent evaporation of an ethanol solution from the synthesis of NaH2sSAE afforded suitable crystals for X-ray diffraction. The X-ray structure, however, reveals that the associated cation is not sodium but rather the ethanol-ammonium arising from protonation of To the best of our knowledge, only two dioxidomolydenum(VI) complexes, the Nsalicylidene-2-aminobenzenethiolato sulfonate dioxidomolydenum(VI) complexes bearing a sulfonated tridentate "ONS" ligand, have been prepared to date as ammonium salts (i.e. with

Me4N + and n-Pr4N + cations) [23]. Unfortunately, these particular complexes were not tested for catalysis and only little is known about their catalytic applicability.

Conversely, tetradentate salen ligands that possess incorporated anionic sulfonato functionalities on the salicylidene backbone have yielded valuable catalysts for oxidation reactions in polar solvents [28]. This observation suggest that our synthesized sulfonated tridentate complexes might also hold potential for catalysis in both water and in ILs, motivating us to screen them in epoxidation reactions using cyclooctene as model substrate.

A first trial was carried out using t-butyl hydroperoxide (TBHP, 70% in water) as oxidant with 3 as catalyst (see Table 4, run 1). The catalyst was entirely soluble in the aqueous phase under our experimental conditions. However, only a modest epoxide yield (i.e.

around 52%) was achieved after 8 hours. An independent 1 H NMR study in D2O revealed that catalyst 3 is decomposed by TBHP. The formation of the salicylaldehyde-5-sulfonate was observed arising from hydrolysis of the Schiff base imine. This product was also seen on the 1 H NMR spectrum of the aqueous phase in D2O taken after the catalytic run.

Considering the tendency of Schiff base ligands and in some cases of the corresponding metal complexes to hydrolyse in water-containing solvent (under certain pH conditions) [29], we then decided to work with decane solutions of TBHP and to perform the catalysis at lower temperature (run 2). Without any additional solvent (other than decane), also low activity towards cyclooctene oxide formation was obtained in the catalytic trial (i.e.

around 46% in epoxide yield after 7.5 h). (b) 55°C 271 62 4 [BMIM][CF3SO3] (b) 55°C 261 10 5 [EMIM][CH3C6H4SO3] (b) 55°C 226 5

6 [BMIM][NTf2]/ [EMIM][CH3C6H4SO3]
(1:4) ( b) 55°C 297 35 (a) TBHP 70 % in water was used with a catalyst: substrate: oxidant ratio of 0.75: 100: 400 (b) TBHP 5.5 M in decane was used with a catalyst: substrate: oxidant ratio of 1: 100: 200

Next, we decided to switch to biphasic conditions in ILs, still using compound 3 as Nevertheless, also an improved influence of the investigated IL systems was observed.

The highest activity was found using the IL [BMIM][NTf2] (run 3, Table 4), although the catalyst solubility is still modest. Thus, like for other literature reports, we find that the catalytic activity can be significantly affected by the nature of the ionic liquid [30]. 4), with the goal to take advantage of the combined increased solubility and activity effects. Although a great increase in solubility was not achieved, the catalytic reactivity was found to be intermediate in As shown in the kinetic profile of Figure 6 for catalyst 3 in [BMIM][NTf2], the sum of cyclooctene oxide and cyclooctene does not add up to a value of 100%, a feature observed for all the biphasic systems described in this report. Additionally, no side products that may account for the difference to 100% were observed by GC/MS analysis. Squares: cyclooctene residual fraction; diamonds: cyclooctene oxide yield.

One explanation could be that the cyclooctene oxide is partially miscible in the IL [BMIM][NTf2] at the reaction temperature. To underline this hypothesis, extraction of the IL phase after the catalytic run (at 270 min) with pentane was envisaged followed by injection of the organic phase into the GC. The measured catalytic fractions (residual cyclooctene and epoxide yield) went respectively from 16 and 66% in the absence of extraction to 14 and 86% by the new procedure. This result shows that, for the cyclooctene oxide, a mass transfer occurs between the two phases during the catalysis because the epoxide is partitioning between the two phases.

Thus far, we presented the synthesis of new ionophilic dioxidomolybdenum complexes and their application in cyclooctene epoxidation in ILs. However, one of the main advantages of using ILs as reaction media is the possibility of reusing the IL phase along with the dissolved or immobilized metal catalyst. Therefore, we studied the recyclability of the most promising catalytic system in our hands, the catalyst 3 in the ionic liquid [BMIM][NTf2] (see Table 5).

Utilization of recycled catalyst showed similar activity in the second cycle. To our surprise we found for compound 3 in the second run even a slightly bigger activity relative to the first cycle. This is likely due to difficulties in the experimental procedure, related to the low solubility of catalyst 3 in the reaction media. Previously, we obtained a 86% yield of epoxide for this reaction (see above). After three consecutive reactions, the catalytic activity decreased significantly to yield only 38% of cyclooctene oxide, probably due to incremental

  reactions were performed in air. Salicylaldehyde, 2-aminophenol, 2-amino-1ethanol, tetrabutylammonium bromide and MoO2(acac)2 (acac = acetylacetonate) were purchased from commercial sources as well as the ionic liquids [BMIM][NTf2] (from Solvionic), [BMIM][CF3SO3] and [EMIM][CH3C6H4SO3] (from Aldrich). Sodium salicylaldehyde-5-sulfonate was synthesized according to literature procedure [16]. 1 H and 13 C NMR spectra were recorded at 200.1 MHz and 50.3 MHz respectively on a Bruker Avance DPX-200 spectrometer. Infrared spectra were recorded on a Mattson Genesis II FT-IR spectrometer using KBr pellets as IR matrix. The catalytic reaction products were analyzed by gas chromatography on an Agilent 6890A chromatograph equipped with FID detector, a HP5-MS capillary column (30 m  0.25 mm  0.25 m) and automatic sampling corresponding to Figure 4 and Figure 6, on a Fisons GC 8000 chromatograph equipped with FID detector and with a SPB-5 capillary column (30 m  0.32 mm  0.25 m) corresponding to Figure 5. Elemental analyses were carried out by the analytical service of the Laboratory of Coordination Chemistry. The analytical results were difficult to interpret because of the uncertainty in the number of water molecules for the sodium salts (compounds 1-4) and possible incomplete combustion (all compounds). The compounds purity is shown by the quality of the NMR spectra (Supporting Information).

  (C-OH); 161.24 (C-OH); 161.39 (CH=N). Selected IR bands (KBr, cm -1 ): 3528(br), 3468(br), 3407(br) ν(OH); 2927(m), 2853(m) ν(C-H); 1621(s) ν(C=N), 1603(sh); 1523(s), 1470(s), 1374(m), 1340(m); 1277(m), 1242(m), 1223(m); 1179(s), 1141(m), 1107(s), 1030(s) ν(SO3 -).

  03 (C aryl); 156.92 (C-O); 160.16 (C-O); 161.33 (CH=N). Selected IR bands (KBr, cm -1 ): 3626(m), 3546(m), 3465(br), 3118(m) ν(OH); 2924(m), 2853(m) ν(C-H); 1617(s) ν(C=N); 1589(m), 1544(m), 1488(s), 1464(m), 1372(m), 1296(m), 1262(s), 1247(m); 1174(s), 1109(s), 1047(s) ν(SO3 -); 933(s), 910(s) ν(Mo=O). FAB-MS: negative mode (M = 420, A -).

  (C aryl); 156.94 (C-O); 160.14 (C-O); 161.0 (CH=N). Selected IR bands (KBr, cm -1 ): 2960(m), 2931(sh), 2872(m) ν(C-H); 1617(s) ν(C=N), 1600(sh); 1585(m), 1546(m), 1491(sh), 1479(m), 1467(m), 1384(m), 1367(m); 1299(s), 1258(s), 1250(sh); 1160(s), 1113(s), 1033(s) ν(SO3 -); 928(s), 903(s) ν(Mo=O). FAB-MS: negative mode (M = 420, A -); positive mode (M = 242, NBu4 + ).

  Scheme 1. Sulfonated tridentate Schiff base ligands NaH2L and the corresponding cis-

Figure 1 .

 1 Figure 1. An ORTEP view of the molecular structure of compound 3. The ellipsoids are

Figure 2 .

 2 Figure 2. On ORTEP view of the molecular structure of compound 5. The ellipsoids are

  Figure 4), those of Anion 2 are correspondingly established with the alcohol part of symmetry

Figure 3 .

 3 Figure 3. An ORTEP view of the asymmetric unit in the structure of

  catalyst and focused on [BMIM][NTf2], [BMIM][CF3SO3] and [EMIM][CH3C6H4SO3]. The two latter sulfonate ILs were chosen for their structural similarity with the sulfonated catalyst, whereas [BMIM][NTf2] was selected because of the high activity already reported for the cyclooctene epoxidation catalyzed by dioxidomolybdenum(VI) complexes [13]. The cyclooctene epoxidation was carried out under the same experimental conditions used in the catalytic trial without the solvent but with the addition of 0.5 mL of IL. The results are presented in Figure 4. The catalyst did not exhibit the expected solubility in the two ILs featuring sulfonate anions. The lowest activity was observed with the ILs [BMIM][CF3SO3] and [EMIM][CH3C6H4SO3] (see runs 4 and 5 in Table 4), likely due to low solubility of the catalyst and high viscosity of the reaction medium, especially in the case of [EMIM][CH3C6H4SO3]. In fact, the obtained data showed even lower activity for the epoxidation in comparison to the control run (run 2 in Table 4) in the absence of any IL in the reaction media. The use of the more conventional [BMIM][PF6] led to an initial small yield of epoxide, followed by its complete disappearance, probably because of diol formation as previously described for other catalysts [13b].

  The best result obtained with the IL [BMIM][NTf2] correlates well with the same activity enhancement observed by Valente et al [13a] and Kühn et al [13b] in the case of their Mo(VI) catalysts in combination with this IL. An additional test was carried out as well in a 1:4 mixture of the ILs [EMIM][CH3C6H4SO3] and [BMIM][NTf2] (run 6, Table

  Figure 4. Comparison of the catalytic activity of 3 in different IL media.

Figure 5 .

 5 Figure 5. Comparison of the catalysts 3 (triangles), 4 (diamonds) and 5 (squares) in cyclooctene epoxidation in [BMIM][NTf 2 ].

Figure 6 :

 6 Figure 6: Kinetic profile for cyclooctene epoxidation with catalyst 3 in [BMIM][NTf2].Squares: cyclooctene residual fraction; diamonds: cyclooctene oxide yield.

  metal loss during the extraction processes. The fifth and final cycle yielded only 19% of cyclooctene oxide. The recycling performance of 3 is comparable to other previously published Mo VI catalysts [13a, 13b].Table 5: Recycling of catalyst 3 in [BMIM]Yield by GC obtained after 270 min of reaction at 55°C.4. ConclusionDiprotic anionic sulfonated Schiff bases (of "ONO"-type) have been assembled by straightforward synthetic procedures that allow the facile introduction of different motifs on the imine function. The corresponding sulfonated Schiff base dioxidomolybdenum complexes have been easily prepared by reaction with the MoO2(acac)2 precursor. They have been engaged in the cyclooctene epoxidation in IL media with TBHP as oxidant. The best catalytic systems are the salts of N-salicylidene-2-aminophenolate sulfonate dioxidomolybdenum(VI),

Table 1 .

 1 Crystal data and structure refinement.

	Identification code	[HOCH2CH2NH3][H2sSAE]	3	5

Table 2 -

 2 Relevant crystallographic distances (Å) and angles (°) for 3 and 5

	Bond lengths	3	5	Angles	3	5
	Mo(1)-O(1)	1.936(1) 1.945(2) O(3)-Mo(1)-O(4) 105.44(7) 105.03(8)
	Mo(1)-O(2)	1.971(1) 1.952(2) O(3)-Mo(1)-O(1) 97.34(6)	95.93(8)
	Mo(1)-O(3)	1.700(1) 1.688(2) O(4)-Mo(1)-O(1) 102.01(6) 101.56(8)
	Mo(1)-O(4)	1.708(1) 1.699(2) O(3)-Mo(1)-O(2) 98.92(7)	98.32(9)

Table 4 :

 4 Epoxidation of cyclooctene catalyzed by 3 in different media

	Run Solvent	Temperature	Reaction	Epoxide
		(°C)	time (min)	yield (%)
	1 Water (a)	80°C	260 480	43 52
	2 No solvent (a)	55°C	279 450	30 46
	3 [BMIM][NTf2]

J HH = 1.7 Hz, 1H, H aryl); 7.81 (m, 1H, H aryl); 8.81 (s, 1H, CH=N).13 C NMR (DMSO-d6,

3 and 5, in the ionic liquid [BMIM][NTf2]. We showed that in the case of catalyst 3 in [BMIM][NTf2], the IL phase along with the immobilized catalyst can be reused for at least three runs with a fairly comparable catalytic activity.


Michel Raous

Constitutive models and numerical methods for frictional contact

Keywords: Friction, Wear, Coating, Oxydation and Corrosion

Validity

The following models are adapted to treat : -unilateral contact, which means that penetration into the obstacle cannot occur and separation is free (the effective contact area depends on the loading), -friction, which means that on the parts of the boundary where contact is established, a frictional force occurs. The formulations and the algorithms are given under the assumptions that : -contact occurs between a deformable body and a rigid obstacle (extension to contact between two deformable bodies is given as a remark), -the deformations are small, -the solid is elastic, -the problem is quasistatic, -adhesion is not involved, -physico-chemical forces are not involved in the contact. Extensions to finite deformations, non linear behaviour, dynamics problems and coupling to adhesion can be found in [1] and in references given in [1].

Models and identification of the parameters

Unilateral contact

Model CI : strict unilateral contact (Signorini conditions)

u N ≤ 0 F N ≤ 0 u N F N = 0              (1)
where F , the unknown contact force density, and u, the displacement defined on the part on the boundary where the contact may occur, are decomposed into normal and tangential components (n is the outward unit vector to the boundary) :

u = u N n + u T , F = F N n + F T .
This satisfactorily describes unilateral contact with the two possible conditions : either no contact, when u N < 0 and F N = 0, or contact, when u N = 0 and F N ≤ 0. This is a non smooth problem, and the complementarity problem (??) implies that F N is a multivalued application of u N , see the graph on Fig. ??. No parameter is needed.

Remark 1 : in the case where an initial gap between the solid and the obstacle has to be considered, u N has to be replaced by (u n -d) where the function d, defined on the boundary, is the initial distance between the solid and the obstacle. When the obstacle moves, the function d is also used to define its movement.

Remark 2 : for the contact between two deformable bodies, in small deformations, a point to point relationship can be used under making a simple change of variables : if A (solid 1) and B (solid 2) are two facing points, let

u A * = u A and u B * = u A -u B .
Model CII : compliance This model allows a penetration which is controlled by a strong reacting force as follows :

F N = -C n (u N ) mn + (2)
where (u N ) + is zero when u N < 0 (no contact), and (u N ) + = u N when u N ≥ 0. This problem is much more regular, because F N is now a function of u N . Its graph is given on Fig. ??. This model is simpler for both computational and mathematical reasons. Nevertheless, some penetration, depending of the choice of parameters C n and m n , occurs.

Identification of C n and m n . A strict identification of C n and m n is not possible. The choice is often made for computational reasons. Mechanical estimates can be obtained by considering the penetration tolerance relatively to the current normal pressure. Considerations on the behaviour of surface asperities, analytically or through computations, can be helpful.

Friction

The general form of a friction law can be written :

F T ≤ f and if F T < f then uT = 0 if F T = f then uT is colinear and opposite to F T              (3)
where various choices for the sliding threshold f can be made.

Model FI : Coulomb law, f = µ | F N |
This is the most classical friction law (µ is the friction coefficient).

Identification of the friction coefficient µ. It is a very difficult matter because, firstly, this coefficient characterizes a pair of materials and, secondly it depends strongly on various conditions (surface machining, temperature, hygrometry, ...). Consequently, tables of friction coefficients are rarely given. As a qualitative indication, it can be said that the range of magnitude is about 0.1 to 0.3 for a metal/metal contact, larger than 1 for contact between rubber and another material and about 0.3 to 0.6 for a wood/wood contact. Specific measurements can be undergone on a sample of the pair of materials by using a tribometer. When it is possible, it is recommended to identify this coefficient on the structure itself by adjusting this parameter, comparing a finite element computation to the experimental result for an elementary loading.

Model FII : Tresca law, f = g The function g is given and defined on the contact boundary. In this case, the sliding limit does not depend on the normal force. This model cannot be directly coupled with unilateral contact. It can be convenient when the normal force is known (polymer injection for example). It is useful in some iterative algorithms used to solve Coulomb problems.

Identification of the function g. When the normal pressure on the contact boundary is known, g is obtained by multiplying it by µ, otherwise, some iterative procedure has to be used to determine a convenient value of the function g on each contact point.

Model FIII : variants -Coulomb-Orowan law, f = min(µ | F N |, k)
The parameter k is usually the elastic limit of the material. It can be used when very high pressures are involved.

-Shaw law, f = αk The function α is defined by α = Γ R /Γ C where Γ R is the nominal (real) contact surface depending on the flattening of the asperities, and Γ C the whole supposed contact surface. This function depending on the normal compression has to be determined either analytically or numerically.

Model FIV : models with a variable friction coefficient A dependence of the friction coefficient on either the sliding velocity (the most classical), the normal pressure, the temperature, or other quantities can be introduced. The Stribeck law (see "Friction in lubricated contacts" by J. Frêne and T. Cicone in this volume) is an example of such a dependence allowing to take into account the transition between dry friction and hydrodynamics regime.

Note : in spite of the attractiveness of this kind of model, one has to be aware of the loss of uniqueness (even for small friction coefficients) and the lack of existence results. This can lead to serious problems in so far as the reliability of the numerical results is concerned.

Model FV : regularized Coulomb law.

A regularized formulation of the Coulomb law is obtained when F T is given as a function of uT (instead of the multivalued application),

F T = -µ ϕ ε ( uT ) | F N |.
For 2D problems, square root, hyperbolic tangent or piecewise polynomial functions are often used. In these cases, a parameter of regularization has to be chosen and the stick situation occurs only when F T = 0.

Model FVI : compliance model.

As in the case of unilateral contact, a compliance law is introduced for the friction law : 3. Numerical methods

F T ≤ C t (u N ) mt + and if F T < C t (u N ) mt + then uT = 0 if F T = C t (u N ) mt + then uT is colinear and opposite to F T              (

Formulations

Both the displacements (unilateral conditions) and the velocities (friction law) are involved. When a displacement formulation is used, an incremental formulation has to be introduced. For each step, a "static" problem will be solved, involving extra terms computed at the previous step and characterizing the memory of the previous loading history. This section focuses on the resolution of this associated "static" problem. The first three formulations concern models using the strict contact relationships (models CI, FI, FII, FIII, FIV), and the fourth formulation is related to models using the regularized contact relationships (models CII, FV, FVI).

An implicit variational inequality

Elimination of the contact forces leads to an implicit variational inequality. For example, a Signorini problem with Coulomb friction can be written as Problem P 1 .

Problem P 1 : For each time t k+1 , find u k+1 ∈ K such that :

a(u k+1 , w -u k+1 )+j(u k+1 , w -u k )-j(u k+1 , u k+1 -u k ) ≥ L k+1 (w -u k+1 ) ∀w ∈ K (5)
where a(.,.) is a bilinear form associated to the elasticity mapping, L(.) is a linear form associated to the current loading, the non differentiable functional j(v, w)(associated to the friction) is j(u, v) = Γ C µ|F N (u)| v T ds and the convex K characterizes the unilateral conditions K = {v ∈ U/ v N ≤ 0 on Γ C } where Γ C is the part of the boundary where contact may occur.

A complementarity problem

An alternative is to write the problem as a linear complementarity problem, introducing two new variables by separating the tangential displacement into left and right sliding. It is then written, after FEM discretization and condensation of the problem to the contact variables (partial inversion of the linear parts), as problem P 2 .

Problem P 2 : Find F ∈ R p , u ∈ R p such that M u = F * + F F i ≤ 0, u i ≤ 0 i = 1 . . . p F i u i = 0 i = 1 . . . p              (6)
where M and F * are respectively a non symmetric matrix and a loading vector deduced from the FEM problem by condensation (and taking into account the change of variables associated to the choice of new variables), F and u are the contact forces and the contact displacements, and p is the number of contact degrees of freedom. This 2D formulation can be extended to 3D problems using a polygonalization of the Coulomb cone.

Lagrange multipliers

Another alternative is based, as for the previous formulation, in keeping the contact forces F as variables (Lagrange multipliers). This time, the unilateral conditions are kept under the form (??) but the friction conditions are written under the Kuhn-Tucker conditions (analogous to plasticity). This is written as problem P 3 where K * is the condensed regular FEM matrix.

Problem P 3 : Find F ∈ R p , ∆ξ ∈ R p such that K * u = F * + F u N ≤ 0, F N ≤ 0, u N F N = 0 f s ≤ 0, ∆u T = -∆ξ ∂f s /∂F T , ∆ξ ≥ 0, ∆ξ f s = 0 f s = F T -µ | F N |                    (7)
A smooth non linear formulation When compliance, regularized models or penalization techniques are used, non linear variational equalities are obtained. Penalization can be considered as a numerical form of the compliance laws previously introduced. The problem is then written in the generic following form.

Problem P 4 : Find u ∈ R p such that :

K * u = F * + φ N (u N ) + φ T (u T ) (8)
where φ N (u N ) is given either by the compliance law (??) or by a penalization (for example (u N ) + ), and φ T (u T ) will be adjusted during the iterations in order to satisfy the Coulomb law.

Algorithms and numerical parameters

For problem P 1 , a fixed point procedure can be introduced to determine the tangential frictional force F T : then, at each step n + 1, we have to solve a Tresca problem with a given sliding threshold g n which can be itself set as the following minimization problem P 1bis , and solution of P 1 is obtained when the process

g n+1 = µ | F N (u n ) | has converged.
Problem P 1bis : Find u n such that J(u n ) ≤ J(v) ∀v ∈ K with :

J(v) = 1/2 a(v, v) -L(v) + Γ C g n v T ds (9)
This minimization problem under constraints ( ∀v ∈ K) of a non differentiable functional can be solved by using various algorithms.

a -Overrelaxation method (SSOR) with projection (Problem P 1bis ) An optimal parameter of relaxation has to be determined by a trial procedure. The method is very robust but can be costly when extension to non linear problems is considered.

b -A Gauss-Seidel method accelerated with an Aitken procedure (Problem P 1bis ) No numerical parameter is needed. Same remark as for (a)can be made.

c -Conjugate gradient method with projection and regularization (Problem P 1bis ) A special procedure is used to preserve the conjugation relationship between the descent directions. Computations of the gradients need a regularization of the friction law which introduces numerical parameters (see model FV). Specific preconditionning has to be used. A regularization parameter is needed.

d -Lemke method (Problem P 2 )

The complementarity problem P 2 is solved by using a mathematical programming method, Lemke method for example. This is a direct mathematical programming method based on pivoting techniques analogous to Simplex methods. It is a very powerful method. No parameter is needed.

e -Augmented Lagrangian with radial return (Problem P 3 ) Problem P 3 is solved with augmented Lagrangian procedure which introduces a penalization by defining :

F N = (λ N -N u N ) (10) ∆F T = ∆λ T -T (u T + ∆ξ ∂f s /∂F T ) (11)
A Newton Raphson algorithm is associated to a radial return procedure. It is analogous to a procedure used in plasticity (even for finite deformations). It is a very powerful method, the accuracy (and also the computational cost) depends on the choice of T , N , and on the number of augmentations performed.

f -Newton-Raphson method for the penalized problem (Problem P 4 ) Problem P 4 is a classical non linear problem where the normal contact force is directly computed during the resolution and the frictional force is adjusted during the iterations in order to verify the Coulomb law. The choice of the penalization parameters (or of the parameters of the compliance law), is delicate because it has a strong influence on the accuracy of the solution (penetration can be large) and on the computational time. Usually, a progressive decrease of the parameters is conducted during the iterations. Accuracy of the solution has always to be checked.

g -Iterative procedure on boundary conditions A simple procedure based on iterations on adjusting boundary conditions in order to verify the unilateral and the friction conditions is sometimes used : at each iterate, u N is set to zero when penetration occurs, uT is first supposed to be zero and, when F T > µ | F N | the previous condition is released but a frictional force is applied, colinear and opposite to uT and such that F T = µ | F N |. Despite the lack of convergence results, this procedure can be efficient for simple linear problems. In other case, the procedure may not converge.

1 -M. Raous, Quasistatic Signorini problem with Coulomb friction and coupling to adhesion, chapter 3 in "New developments in contact problems", P. Wriggers-P.Panagiotopoulos (Eds), CISM Courses and Lectures, n 384, Springer Verlag, Wien-New York, 1999, pp. 101-178

Figure 1 :

 1 Figure 1: Graph of the Signorini law Figure 2: Graph of the compliance law

Figure 3 :

 3 Figure 3: Graph of the Coulomb law (in 2D) Figure 4: Various friction laws (in 2D)