Ali Mokh

Ramin Khayatzadeh

Julien De Rosny

Mohamed Kamoun

Abdelwaheb Ourir

Arnaud Tourin

Mathias Fink

Indoor Experimental Evaluation of Ultra-wideband MU-MISO TRDMA

Keywords: Time-Reversal, Multi-user MISO (MU-MISO), TRDMA, Wave focusing, Beamforming

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I. INTRODUCTION

A Time reversal mirror is an apparatus to focus wave both in time and in space. It is based on the time-reversal symmetry of propagating media. Thirty years ago, it has been first applied to focus ultrasonic waves in water, tissues, solids. Time Reversal mirror is very efficient in complex media such as multiple scattering media [1] or cavities [START_REF] Draeger | One-channel time reversal of elastic waves in a chaotic 2d-silicon cavity[END_REF] because it takes benefit of the reflections to enhance the focusing. In acoustics, the main application of time reversal is non-destructive control, imaging, therapy [START_REF] Fink | Time-reversed acoustics[END_REF]. In 2004, the concept of time reversal mirror has been extended to microwave [START_REF] Lerosey | Time reversal of electromagnetic waves and telecommunication[END_REF] at 2.4GHz. Because the larger the bandwidth, the better the focusing, two years later, a wide-band time reversal was successfully performed [START_REF] Lerosey | Time reversal of wideband microwaves[END_REF].

Telecommunication is a natural application field of time reversal mirrors. As soon as the early 2000s, an acoustic time Reversal mirror has been used to transmit bits between two vessels in a shallow water environment near Elba island [START_REF] Edelmann | An initial demonstration of underwater acoustic communication using time reversal[END_REF]. Indeed, the temporal pulse compression mitigates the intersymbol interference (ISI) resulting from multipath propagation, while the spatial focusing reduces inter-user interference (IUI) [START_REF] Oestges | Time reversal techniques for broadband wireless communication systems[END_REF].

Soon after, the interest of time reversal for radio communications appeared. Inside an urban environment, [START_REF] Kyritsi | Miso time reversal and delay-impulse radio uwb communications based on time reversal technique[END_REF] has shown a delay spread reduction of up to a factor of 3. In the case of a mild multipath environment, a good spatial and temporal focusing gain is reached using a transmitter with a sufficiently large number of antenna [9].

Recent research in wireless communications has frequently been focusing on UWB due to its potential in short-range communications and positioning applications thanks to its ability effectively collect energy that is dispersed in rich multipaths [10]. Moreover non-coherent receivers can be used for low-cost and low-power sensors [11], [12], TR is especially suited for UWB Internet-of-Things [13].

In terms of communication theory, TR is a downlink precoding technique both for SISO and MU-MISO impulse radio UWB (IR-UWB) wireless communication [14].

A few years ago, TRDMA has been introduced to focus messages to different users (MISO-MU configuration) [START_REF] Han | Timereversal division multiple access over multi-path channels[END_REF]. TRDMA provides a cost-effective single-carrier alternative with high power efficiency [START_REF] Lienard | Focusing gain model of time-reversed signals in dense multipath channels[END_REF], for downlink and uplink transmission [START_REF] Han | A multiuser TRDMA uplink system with 2d parallel interference cancellation[END_REF]. Theoretical analysis for the average signalto-noise ratio (SNR) of the intended and unintended receivers in a distributed TR transmission scheme was analysed in [START_REF] Wang | Snr analysis of time reversal signaling on target and unintended receivers in distributed transmission[END_REF], while a probabilistic analysis (probability density function) of the SNR at the receiver in a TR communication was derived in [START_REF] Lei | Performance analysis of time reversal communication systems[END_REF], and then the ergodic capacity and theoretical bit error rate (BER) when phase-shift keying (PSK) modulation is used was also obtained.

For summary, the works in the state of art has focused on the theoretical analysis of TRDMA system. While experimental studies have been performed in a SISO (eg. [START_REF] Naqvi | Experimental validation of time reversal ultra wideband communication system for high data rates[END_REF]) or MIMO configuration [START_REF] El-Sallabi | Experimental investigation on time reversal precoding for space-time focusing in wireless communications[END_REF]. However to the best of our knowledge, no experimental study has been performed to test TRDMA in real indoor environments.

In this paper, we evaluated the performance of UWB MISO TRDMA, experimentally and in simulation for indoor transmission for the first time to the best of our knowledge. An experimental setup with an 8 antenna TR base station and 2 single-antenna users is deployed inside a small office. After a channel sounding sequence, the channel is flipped in time and phase conjugated. These signals are sent back by the TR array toward each user and the IUI is probed. These TR focused signals are used to simulate TRDMA communication. The BER is evaluated for different settings.

The rest of the paper is organized as follows. In section II, the principle of TRDMA is restated, and we explain the input-output equations for MISO-TRDMA. In section III, the experimental setup of MISO TRDMA is presented, followed by the explanation of the channel sounding method. Then the focused signals are shown on each user when estimated channels are time-reversed. Finally, the simulation block diagram and TRDMA simulation results are provided in Section IV.

II. TIME REVERSAL DIVISION MULTIPLE ACCESS (TRDMA)

This section introduces the model and notations for MU-MISO time reversal (TR) for multi-user scenarios.

A. Time Reversal

Let us consider a MU-MISO transmission system, composed of one transmitter equipped with M transmit antennas and N users with single antenna each. We note h i,m [k] the complex tap at tap time index k of the base-band channel impulse response (CIR) between the m-th transmit antenna and the i-th user. We assume that the CIRs vanishes after L complex taps, i.e, |L[k]| > 0 for 0  k  L 1. TR precoding consists in using the flipped and conjugated impulse response (CIR), i.e.,

g i,m [k] = h ⇤ i,m [ k],
as transmitting filter. In a MU-MISO scenario, the received signal y j after TR precoding for user j read, when focusing towards user i is

y j [k] = (x ⇤ R ji )[k] p R ii [0] + n j [k]. ( 1
)
where x is the transmit signal, n j is an additive white Gaussian noise with standard deviation , ⇤ is the discrete convolution operator and R j,i be the correlation function between the CIRs of users j and i. This last is given by

R ji [k] = [k] M X m=1 L 1 X l=0 h ⇤ i,m [l]h j,m [l] + M X m=1 L 1 X l=0 L 1 X p=0,p6 =l h ⇤ i,m [l]h j,m [p] [k (p l)] | {z } ISI,IUI . (2)
Note that the correlation function is a time symmetric function, i.e., R ii

[ k] = R ⇤ ii [k]
. At k = 0, the correlation function is maximum and real. With multi-path channels, when applying TR precoding with the CIR of user i, the time-reversed field focuses in time and in space (in user i location) [START_REF] Fink | Chaos and time-reversed acoustics[END_REF] with a peak given by the auto-correlation function R i,i [0]. Indeed at this time and location, M ⇥ L signals add coherently. This coherent combination is corrupted by random interference that generate ISI (k 6 = 0) and IUI (i 6 = j).

III. MISO TRDMA EXPERIMENT SETUP AND RESULT

A. Experiment Setup

To evaluate the MISO-TRDMA scheme, we use an experimental setup to sound the channel and time reverse the signals (see figure 1). It is composed of a transmitter array with M = 8 antennas, all connected to a solid-state RF switch. The input of the 1x8 switch is connected to an RF amplifier that is fed by an Arbitrary Waveform Generator (AWG) from Tektronix (AWG-7012). This last is used to generate the signal

B. Channel Estimation And Time Reversal

Channel estimation and time reversal are mainly done in 3 steps. First, a chirp signal c(t) with carrier frequency of f c = 2GHz and bandwidth of B is emitted through the channel using an RF switch and 8 TX antennas. The received RF signals are sampled using the digital oscilloscope and recorded into the computer. The 8x2 CIR is estimated by correlating the 8x2 received signals with c(t). Note that the emission and the reception are directly performed in the RF band. The CIR is flipped in time and resampled to change the sampling frequency from 12.5 GHz to 10 GHz. Each TR CIR is then sent back from the corresponding TX antenna, i.e., for instance, the CIR recorded between the 3rd Tx antenna and the second Rx antenna, is sent back by the 3rd Tx antenna. At the end, the TR signals are recorded on the 2 Rx antennas and down-converted to store the baseband signals.

C. Results

Since in this experiment we are using a switch between transmit antenna, each signal is transmitted separately. So to emulate MISO TRDMA, we added all received signals from different transmit antennas, when targeting specific receive antenna, and normalized the sum by 1/ p M to maintain the same average transmit power.

Figure 2 shows the baseband MISO TR received signal at antenna R1 and R2 with 800 MHz bandwidth in multi-user scenario when targeting either antenna R1 or R2. For sake of simplicity, the origin of time in these figures is considered to be at the peak of the time-reversed receive signal (i.e. where R[0] is the maximum), so that the autocorrelation function is a pair function as shown in equation [START_REF] Fink | Time-reversed acoustics[END_REF]. Depending on the targeted antenna, we can observe that the focused amplitude is 8 dB and 15 dB higher than on the other antenna. The IUI is due to the imperfect spatial focusing of TR. In the next section, those signals are used in a simulation chain to simulate TRDMA and observe the performance of the proposed system.

IV. TRDMA SIMULATION

A. TRDMA Simulation Scheme Figure 3 shows the block diagram of the simulated transmission chain of MISO TRDMA based on the measured signals.

The binary data for each user are PSK modulated in order to keep the amplitude of the signal fixed, so that we can analyze the effect of the interference on the transmission in different conditions, and the resulting I/Q signals are convoluted with the TR focusing signal. This last can be seen as the timereversed channel. On each channel, the measured interference is added. At each receiver, the received signal contains the sum of the focused signal and the inter-user interference from the signal transmitted to the other user. This received signal is demodulated with a simple phase detector that estimates the PSK symbol that has the closest phase to the received signal. We counted the error rate by comparing the transmit and detected information.

B. Simulation Results

Let introduce n as the number of taps between the symbols, the symbol rate is then given by B/n and m is the order of PSK modulation. The simulation is run for different order m of PSK modulation. Complex White Gaussian Noise is added to the received signal where the standard deviation is related to the SNR and the amplitude of the central path. Figure 4 represents the BER for the maximum bandwidth, i.e., 800MHz, and at SNR=20 dB for both users. Results show that the smaller the order of modulation or the larger the number of taps between symbols, the smaller the BER. Also, for QPSK modulation, a transmission with BER smaller than 10 4 could be achieved for symbol spacing n = 2, since the effect of ISI becomes negligible. However, because of the IUI, even with large symbol spacing, a minimum BER that is higher than 10 2 , respectively higher than 10 2 , could not be reduced for 8-PSK modulation, respectively for 16-PSK modulation, using a simple phase detector. In figure 5, the BER in terms of SNR is plotted. We fixed the symbol spacing at n = 2, and we used different order of modulation (from BPSK to 16-PSK). It is shown that for an SNR less than 20 dB, both BPSK and QPSK could be used with BER less than 10 3 , and an 8-PSK modulation could be implemented with a BER less than 10 3 for SNR=30dB. This is suitable for low complexity devices since no post-processing is needed. But even with such SNR, the 16-PSK modulation still around 10 1 , because of the effect of interference. In figure 6, the effect of the bandwidth on the transmission is evaluated. The BPSK modulation is considered for all simulations, and we measured the BER in terms of number of taps between the symbols for B = 100 MHz, 200 MHz and 400 MHz, only for the first user, and also for SNR=10 dB. The results show that the higher the bandwidth, the more efficient the TR transmission, since the temporal focusing gain increases. Actually, this is reffered to the fact that the higher the bandwidth, the more the system can estimates channel taps during the same symbol duration, and from equation (3), one can see that the grater the number of taps L, the grater the amplitude of the central peak (k=0). Also, by increasing n the BER decreases until it reaches a plateau which is caused by the IUI.

V. CONCLUSION

In this paper, we evaluated experimentally and by a simulation the performance of an UWB MISO TRDMA system for multiuser scenario. Results show that by increasing the time difference between symbols, the effect of the ISI could be reduced, but the IUI still limiting the performance of the system. In addition, the greater the bandwidth is, the more robust the transmission becomes. We can conclude that the TR precoding is suitable in multi-access transmission for multiuser scenario, mainly for low complexity devices in multi-path channel environment as indoor transmission.

Fig. 1 .

 1 Fig. 1. MISO TRDMA Experimental Setup

Fig. 2 .

 2 Fig. 2. MISO TR received signal and IUI at R1 and R2 when targeting R1 or R2

Fig. 3 .Fig. 4 .

 34 Fig. 3. MISO TRDMA simulation chain

Fig. 6 .

 6 Fig.6. BER Vs number of taps (n) of the first user using TRDMA for different bandwidth

  5. BER Vs SNR of one user for different PSK order of modulation using MISO TRDMA with B=800MHz, with n = 2 spread compression for fwa channels at 5 ghz," IEEE Antennas Wireless Propag. Lett., vol. 3, no. 1, pp. 96-99, 2004. [9] S.-Q. Xiao, J. Chen, X.-F. Liu, and B.-Z. Wang, "Spatial focusing characteristics of time reversal uwb pulse transmission with different antenna arrays," Prog. Electromagn. Res, vol. 2, pp. 223-232, 2008. [10] H. T. Nguyen, J. B. Andersen, and G. F. Pedersen, "The potential use of time reversal techniques in multiple element antenna systems," IEEE Commun. Lett., vol. 9, no. 1, pp. 40-42, jan 2005. [11] B. Wang, Y. Wu, F. Han, Y.-H. Yang, and K. J. R. Liu, "Green wireless communications: A time-reversal paradigm," IEEE J. Sel. Areas Commun., vol. 29, no. 8, pp. 1698-1710, sep 2011. [12] Y. Chen, Y.-H. Yang, F. Han, and K. J. R. Liu, "Time-reversal wideband communications," IEEE Signal Process. Lett., vol. 20, no. 12, pp. 1219-1222, dec 2013. [13] Y. Chen, F. Han, Y.-H. Yang, H. Ma, Y. Han, C. Jiang, H.-Q. Lai, D. Claffey, Z. Safar, and K. J. R. Liu, "Time-reversal wireless paradigm for green internet of things: An overview," IEEE Internet Things J., vol. 1, no. 1, pp. 81-98, feb 2014. [14] X.-F. Liu, B.-Z. Wang, S.-Q. Xiao, and J. H. Deng, "Performance of


Tony Cousin

Gregory Chatel

Bruno Andrioletti
email: bruno.andrioletti@univ-lyon1.fr

Micheline Draye
email: micheline.draye@univ-smb.fr

Oxidative cleavage of cycloalkenes using hydrogen peroxide and a tungsten-based catalyst: towards a complete mechanistic investigation

come

Oxidative cleavage of cycloalkenes using hydrogen peroxide and a tungsten-based catalyst: towards a complete mechanistic investigation

Introduction

The oxidative cleavage of C=C bonds has witnessed a growing interest for several decades as a key transformation to access value-added mono-and dicarboxylic acids from olefins. 1-5 More specifically, dicarboxylic acids are major intermediates for the manufacture of important polyesters and polyamides materials but also for the production of daily products found in a wide range of applications such as lubricants, fibers, cosmetics, pesticides, pharmaceuticals and plasticizers. [START_REF] Cornils | Ullmann's Encyclopedia of Industrial Chemistry[END_REF][START_REF] Musser | Ullmann's Encyclopedia of Industrial Chemistry[END_REF] In the chemical industry, this class of compounds is mainly obtained by oxidative cleavage of unsaturated carboxylic acids and cycloalkenes. [START_REF] Cornils | Ullmann's Encyclopedia of Industrial Chemistry[END_REF][START_REF] Musser | Ullmann's Encyclopedia of Industrial Chemistry[END_REF] One of the oldest oxidative cleavage process was patented by DuPont in the 50s for the production of adipic acid. Since, this dicarboxylic acid is still manufactured via the aerobic oxidation of cyclohexane to cyclohexanol and cyclohexanone followed by the oxidative cleavage of either one or a mixture of both (ketone + alcohol = KA Oil) with nitric acid. [START_REF] Hamblet | [END_REF] This industrial process leads to the formation of adipic acid in 95% yield with an annual production of 4 million tons.

7,9

Adipic acid production is mainly dedicated to the synthesis of nylon 6,6 but also to plasticizers, lubricants and polyurethane resins.

7,10

Despite the major importance of adipic acid for key applications, the DuPont process results in the production of large volumetric amounts of nitrous oxide. Actually, up to 400,000 metric tons of N 2 O arise from the oxidative cleavage of KA Oil by nitric acid, representing 8% of the total anthropogenic production of this greenhouse gas. 11,12 Nitrous oxide is particularly harmful towards the environment as it causes ozone depletion, smog, acid rains and its global potential warming is 300 times higher than CO 2 . [13][14][START_REF] Reimer | Non-CO 2 Greenhouse Gases: Scientific Understanding, Control and Implementation[END_REF][START_REF] Cavani | Sustainable Industrial Chemistry[END_REF] Even if efforts to reduce the amount of released N 2 O through recycling, thermal and catalytic decomposition [START_REF] Bart | [END_REF]14,[START_REF] Cavani | Sustainable Industrial Chemistry[END_REF][START_REF] Shimizu | [END_REF] have been done, the energy consumption for adipic acid production remains high because this multi-step reaction is performed at temperatures reaching up to 160 °C. 7,8,13 These observations have prompted researchers to develop more environmentally-friendly routes for the production of dicarboxylic acids through cycloolefin oxidative cleavage. In this context, hydrogen peroxide has been considered to replace commonly used oxidants. Indeed, H 2 O 2 presents many advantages for the development of greener oxidation reactions: it is a widely available oxidant with 47% of active oxygen content, non-toxic, only releases water as theoretical by-product and does not require temperatures above 100 °C to perform oxidations. [START_REF] Jones | Applications of hydrogen peroxide and derivatives[END_REF][START_REF] Ciriminna | [END_REF] The H 2 O 2 -mediated oxidative cleavage of cycloalkenes has been widely documented in the literature. The last trends in the development of sustainable catalytic systems for this reaction have been recently reviewed. 5 In particular, the use of hydrogen peroxide in association with tungsten-based catalysts has shown to be a promising combination to decrease the environmental impact of the cycloalkene oxidative cleavage. Indeed, compared to other transition metals used for this reaction, tungsten-based catalysts are low cost, [START_REF] Horwitz | Innovations in Green Chemistry and Green Engineering[END_REF][START_REF] Lassner | Ullmann's Encyclopedia of Industrial Chemistry[END_REF] non-toxic [START_REF]Handbook of toxicology[END_REF][START_REF] Leffler | Handbook on the Toxicology of Metals[END_REF] Please do not adjust margins Please do not adjust margins produce peroxotungstate compounds highly active toward olefins.

24,25

Scheme 1: Oxidative cleavage of cycloalkenes with H2O2 and a tungsten-based catalyst according to Noyori.

11,26

Among the numerous studies dealing with H 2 O 2 -mediated cycloalkene oxidative cleavage with tungsten-based catalysts, a large majority of publications exposes the reaction mechanism suggested by Noyori et al. 11,26 for rationalizing the formation of dicarboxylic acids from cycloalkenes (Scheme 1). This mechanism involves six reaction steps including an alkene epoxidation, an epoxide hydrolysis, a first alcohol oxidation, a Baeyer-Villiger oxidation, a second alcohol oxidation and a cyclic anhydride hydrolysis (Scheme 1). Even if intermediates 2 to 4 have been unambiguously identified and described in the literature, the production of intermediates 5 and 6 through Baeyer-Villiger enlargement have not been highlighted yet. Their presence in the oxidation mechanism has been so far justified through indirect studies and computational modelling.

27-29

No complete mechanism has been established to date to explain the formation of the targeted dicarboxylic acid from the hydroxy-ketone intermediate 4. Moreover, among studies on the oxidative cleavage of cycloolefins, several by-products are often observed along with the expected dicarboxylic acid. Indeed, from 1 to 5% of additional dicarboxylic acids, shortened by 1 to 3 carbon atoms compared to the targeted one, are observed at the end of the reaction. 11,30,31 Despite their occurrence in studies, no hypothesis for their formation has been suggested so far. The accurate comprehension of the reaction pathways for product and by-products formation is of prime interest to determine the conditions favouring the production of the targeted dicarboxylic acid and minimizing the formation of these by-products.

In this study, we aim at confirming and completing the mechanisms proposed in the literature for the oxidative cleavage of cycloalkenes with H 2 O 2 and a tungsten-based catalyst through the structural determination of intermediates and by-products of the reaction. Studies of the reaction at different stages and under different experimental conditions allow highlighting the structure and amount of by-products formed during the reaction.

Experimental

All chemicals were used without further purification and purchased from Acros, Aldrich, Alfa Aesar, Honeywell and Fluka.

Gas chromatography was performed on a HP 6890 Series gas chromatograph from Hewlett Packard using a flameionization detector and equipped with an Optima-5MS Accent capillary column (dimethylpolysiloxane, 30 m x 0.25 mm x 0.25 µm) from Marcherey Nagel. All analyses were undertaken with helium as carrier gas (24 mL.min -1

) in split mode (split ratio: 1:40) and an injector and a detector both heated at 290 °C.

Mass spectra were recorded on an Agilent 5973 N Mass Selective Detector coupled to an Agilent 6890 GC and equipped with an Optima 5 capillary column (dimethylpolysiloxane 30 m x 0.32 mm x 0.25 µm) from Macherey-Nagel.

Cyclohexene oxidative cleavage

The reactions were performed following the procedure described in the reference study. 11,26 Hydrogen peroxide (35 wt.%, 2.6-525 g, 4.4 eq.) was added to a mixture of tungstenbased catalyst (1 mol%) and Phase Transfer Catalyst (PTC: Aliquat 336® or Oct 3 MeN + HSO 4 -, 1 mol%) into a round bottom flask. The solution was vigorously stirred with a magnetic stirring bar at room temperature for 10 min to solubilize as much of catalyst as possible. After addition of cyclohexene (0.5-100 g, 1 eq.), the round bottom flask was equipped with a condenser and successively heated to 75 °C for 30 min, 80 °C for 30 min, 85 °C for 30 min, and 90 °C for 6 h 30 min while stirring at 1,000 rpm. After 8 h, the reaction medium was cooled to room temperature before being placed at 5 °C overnight. Then, the resulting white precipitate was separated from the aqueous solution by filtration, washed 3 times with cold deionized water and dried under reduced pressure. Sodium sulphite was added portion-wise to the aqueous filtrate until complete decomposition of remaining hydrogen peroxide. After acidification with sulfuric acid to pH = 1, water was then evaporated under reduced pressure and 20 mL acetone was added to the solid residue. After separation of the organic solution from inorganic salts by filtration, acetone was eliminated under reduced pressure. Solid residues from the aqueous filtrate and precipitated adipic acid were analyzed by gas chromatography for quantification of all reaction products by internal standard method (dodecane used as internal standard) after derivatization with N-Obis(trimethylsilyl)trifluoroacetamide for 2 h at 50 °C. Reaction by-products were identified by GC/MS (characterization is available in ESI †).

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Cycloalkene epoxidation

The cyclopentene, cyclohexene and cyclooctene epoxidations were performed as follows. Into a 250 mL round bottom flask, an aqueous solution of hydrogen peroxide (280 mmol, 26.90 g, 1.5 eq., 35 wt.%) was added to a mixture of H 2 WO 4 (1.4 mmol, 0.346 g, 0.75 mol%) and Aliquat 336® (1.4 mmol, 0.56 g, 0.75 mol%). The aqueous solution was stirred at room temperature with a stirring bar for 10 min before adding the cycloalkene (185 mmol). The round bottom flask was equipped with a condenser before stirring the biphasic mixture at 80 °C without any incubation period at 1,000 rpm for 30 min. At the end of the reaction, the aqueous phase was separated from the organic layer, thoroughly extracted by CH 2 Cl 2 or diethyl ether (3 x 30 mL) in order to recover remaining cycloalkene and newly formed products, and concentrated under reduced pressure. Isolation and analysis of nonextracted epoxidation by-products contained into the aqueous phase were undertaken according to the same procedure as previously. Reaction by-products were identified by GC/MS (characterization is available in ESI †).

Results and discussion

Within the scope of our study, we decided to limit our investigations to cyclohexene, cyclopentene and cyclooctene for the epoxidation and to cyclohexene for the oxidative cleavage. Indeed, the oxidative cleavage of cycloolefins is welldescribed in the literature on these small-sized cycloalkenes and affords the dicarboxylic acids with over 75% yields. 5 Besides, the reaction performed on larger rings such as cyclooctene and cyclododecene results in low yields, generally below 30% because of transannular reactions occurring on the epoxide derivatives of these medium-sized cycloalkenes.

5,32

Among the studies on the oxidative cleavage of cyclic alkenes with H 2 O 2 and a tungsten-based catalyst, those from Noyori and co-workers are still a reference in terms of green chemistry. Indeed, the reaction conditions involve 4.4 equivalents of 30% H 2 O 2 , 1 mol% of Na 2 WO 4 and Oct 3 MeN + HSO 4 -as a Phase Transfer Catalyst (PTC). These conditions allow to perform the oxidative cleavage of 100 g of cyclohexene from 75 to 90 °C in 8 h and without any organic solvent. Adipic acid is isolated in 93% yield.

11,26

During our studies, the oxidative cleavage of cyclohexene was investigated under the conditions described by Noyori and co-workers. The production of adipic acid as well as the byproducts was followed by gas chromatography (GC). At first, the reaction was studied under the conditions used for the oxidative cleavage of 100 g of cyclohexene, corresponding to 600 mL of reaction volume, 11,26 and on 8 and 3 mL scales in order to decrease the amounts of reactants used per run. The obtained results are gathered in the Table 1.

At 600 mL reaction scale, the oxidative cleavage of cyclohexene leads to 83% adipic acid yield (Table 1, Entry 2) instead of the 93% published in the literature (Table 1, Entry 1). These results can be ascribed to the formation of 1,2-cyclohexanediol, 2-cyclohexanone and glutaric acid observed in 0.5 to 4.5% yields. Moreover, the reaction performed under Noyori's conditions revealed the formation of by-products that were not described in the original work. Thus, little amounts (< 0.5%) of 5-hydroxypentanoic, 5-oxopentanoïc and succinic acid were detected during our study. When the reaction volume was decreased from 600 mL to 8 mL and 3 mL, the yield of adipic acid decreased from 83% to 47% and 39% respectively (Table 1, Entries 2, 3 and 4). However, the same by-products were produced in similar yields than with 600 mL reaction volume, leading to an unsatisfactory mass balance. Hence, the oxidative cleavage yields and selectivities lower than 50% observed with reaction volumes below 10 mL can be explained by a cyclohexene loss by volatilization during the 8 h of reaction. Indeed, despite the experimental care, some of the solution has been volatilized. This would explain the choice of 100 g of starting cycloalkene chosen in the reference study, 11,26 that ensure a minimum impact of volatilization of the reactant on the yield of the reaction. A reaction volume of 8 mL was chosen for the rest of the study, guaranteeing a reasonable yield and the use of a minimum amount of reactants (Table 1, Entry 3). Based on the initial amount of cyclohexene and calculated by GC with internal standard method.

d By-products detected by GC/MS †. e Results from the reference publication.

11,26

Then the oxidative cleavage of cyclohexene was studied with different associations of tungsten-based catalysts and PTC following the formation of by-products. In addition, H 2 WO 4 /Aliquat 336 ® was chosen as catalytic system as it affords yields above 80% for the oxidative cleavage of cyclohexene and cyclopentene in the literature. 30,33 Different combinations of W-based catalyst and PTC were studied in order to reach a pH < 3 in the reaction medium. Indeed, a pH below 3 is required to ensure the formation of the active catalytic species 26,[34][35][36] and to prevent H 2 O 2 from catalytic and thermal decomposition.

18,19,37

Thus, the combination Na 2 WO 4 /Aliquat 336 ® was not selected as it affords a pH of 6 in the reaction medium. The results obtained with the different catalytic compositions are summarized in the Table 2. c Based on the amount of converted cyclohexene and calculated by GC with internal standard method.

Based on the initial amount of cyclohexene and calculated by GC with internal standard method. e By-products detected by GC/MS †.

f 1,2-cyclohexanediol yield.

Among the catalytic systems that have been studied, the combination of tungstic acid with Aliquat 336 ® led to the highest results with an adipic acid yield of 59% (Table 2, Entry 2). Under these conditions, the major intermediate is the 1,2cyclohexandiol with a yield of 15%. The GC/MS analyses of the different runs revealed the formation of by-products of identical structure and in similar amount as previously (Tables 1 and2). In order to assess a complete mechanism, the initial alkene epoxidation using H 2 WO 4 and Aliquat 336 ® has been investigated.

In a very recent study, we showed that this system combined to high frequency ultrasound particularly improved the epoxidation of cis-cyclooctene and revealed important mechanistic insights of the studied reaction. [START_REF] Cousin | [END_REF] Hence, under 800 kHz ultrasonic irradiation, in the presence of 0.75%mol of H 2 WO 4 and Aliquat 336 ® and 1.5 eq. of 30% H 2 O 2 related to the substrate, 96% yield of epoxide was obtained with 98% selectivity within only 30 min. In addition, the non-radical nature of cis-cyclooctene epoxidation mechanism has been demonstrated. [START_REF] Cousin | [END_REF] In the present study, under magnetic stirring, the chosen oxidizing system leads to epoxycyclooctane in 89% yield and 91% selectivity (Table 3, Entry 1). The same conditions have been then used for the epoxidation of cyclohexene and cyclopentene (Table 3, Entries 2 and 3) and the structural identification of the products issued from the oxidation of these three cycloalkenes have been performed (Table 3). Unfortunately, in spite of the excellent epoxidation results observed with cis-cyclooctene, the oxidizing system was not efficient to selectively convert cyclohexene and cyclopentene to their corresponding epoxides in 30 min. Indeed, while cyclooctene is almost fully transformed to epoxycyclooctane in 89% yield (Table 3, Entry 1), conversion of smaller cycloalkenes did not exceed 75% and their epoxides were observed in 0 and 3% yields (Table 3, Entries 2 and 3). These results are explained by the higher reactivity of the double bond of cyclooctene toward electrophilic oxidants compared to the one of other cycloalkenes and the strong resistance of its epoxide toward hydrolysis under acidic conditions. 11,32,39 Indeed, this particular reactivity of medium-sized cycloalkenes such as cyclooctene has been attributed to transannular reactions occurring during solvolysis of their oxides, and which is related to the spatial proximity of the opposite sides of their medium-sized ring. Please do not adjust margins

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The few by-products observed for cyclooctene epoxidation are its oxidative cleavage intermediates 1,2-diol and αhydroxyketone, a 1,4-diol formed from transannular reaction, and a product of allylic oxidation, 2-cyclooctenone (Table 3, Entry 1). With cyclohexene and cyclopentene, reaction conditions mainly led to the production of their corresponding 1,2-diols with 39 and 32% yield respectively (Table 3, Entries 2 and 3). Numerous by-products arising from the oxidation of these cycloolefins were also formed with yields below 2%.

Among them, oxidative cleavage products and known intermediates, previously observed in this work, such as αhydroxyketone and dicarboxylic acid have been detected (Table 3, Entries 2 and 3).

Scheme 2: Mechanism for the oxidative cleavage of cyclohexene and the production of dicarboxylic acids of shorter carbon chain in the presence of H2O2 and a tungsten-based catalyst.

The oxidation of cyclopentene also revealed the formation of additional by-products such as 4-oxobutanoïc and 4-This journal is © The Royal Society of Chemistry 2020

Please do not adjust margins Please do not adjust margins formyloxobutanoïc acids (Table 3, Entry 3). In order to understand the formation of the by-products observed during the different steps of the oxidative cleavage of cycloalkenes, their structure was determined and compared to the results described in the literature. The present study on the oxidative cleavage and epoxidation of cyclohexene and cyclopentene allows highlighting the formation of 2 categories of compounds: oxidative cleavage intermediates and by-products.

On the one hand, expected reaction intermediates such as epoxide 2, 1,2-diol 3, and hydroxy-ketone 4 have been identified (Tables 1, 2 and3). Despite the different reaction conditions and analyses carried out within the frame of our studies, the hydroxy-lactone 5 and cyclic anhydride 6 proposed by Noyori have never been detected. (Scheme 1). [START_REF] Hassall | Organic Reactions[END_REF][START_REF] Krow | Organic Reactions[END_REF] is able to rearrange to both the mono-aldehyde 9 and the hydroxylactone 5 via a Baeyer-Villiger mechanism (Schemes 2 and 3). 29,[START_REF] Hassall | Organic Reactions[END_REF] Mechanisms proposed by Noyori and Venturello have been combined to complete the reaction scheme suggested by Noyori (Scheme 1).

In their studies on the oxidative cleavage of 1,2cyclohexanediol derivatives, Fujitani and co-workers 41 proposed the production of a gem-dihydroxy acid (10 in Scheme 2) to explain the presence of the Baeyer-Villiger product 5 suggested by Noyori, and the formation of the hydroperoxyalcohol 8 and mono-aldehyde 9 suggested by Venturello. 42 Nevertheless, none of these three intermediates were detected in our studies. It is worth noting that Noyori's hydroxy-lactone 5 is the result of Venturello's mono-aldehyde 9 cyclization. Thus, regarding the numerous interconnexions existing between the above-mentioned intermediates, both pathways described in Scheme 2 should be considered to rationalize the formation of dicarboxylic acids from cycloolefin oxidative cleavage. On the other hand, the by-products formed from sidereactions on oxidative cleavage intermediates have also been identified in this work during epoxidation and oxidative cleavage of cycloalkenes (Tables 1, 2 and3). More specifically, dicarboxylic acids with 1 to 3 less carbon atoms compared to the targeted product have been mainly identified during epoxidation and oxidative cleavage studies. This category of by-product is often observed in the literature but no explanation has been brought to date to justify their formation. One reaction pathway that could lead to these shorter diacids could involve a decarboxylation of the desired dicarboxylic acid. 4 Nevertheless, thermal decarboxylation of dicarboxylic acids mainly occurs at temperatures above 290 °C6 and usually leads to the corresponding alkanes. Besides, it was shown in the literature that α-oxoacids can afford diacids shortened by one carbon by decarboxylation in the presence of H 2 O 2 .

48

The production of shorter dicarboxylic acids could be explained by a H 2 O 2 -mediated Baeyer-Villiger oxidation of the mono-aldehyde intermediate 9. Indeed, while the reaction between an aldehyde and hydrogen peroxide generally leads to the formation of the corresponding carboxylic acid, the nucleophilic addition of H 2 O 2 on the aldehyde gives rise to a high-energy hydroperoxyalcohol intermediate that rearranges into formate ester (Scheme 4). [START_REF] Jones | Applications of hydrogen peroxide and derivatives[END_REF]43,[START_REF] Hassall | Organic Reactions[END_REF][START_REF] Krow | Organic Reactions[END_REF] The formation of the carboxylic acid and the formate ester from the rearrangement of the Criegee intermediate can take place via the nucleophilic addition of either H 2 O 2 or peroxotungstate complexes to the mono-aldehyde. [START_REF] Venturello | [END_REF] Once formed, the formate ester (Scheme 2, 11) is next hydrolysed to the alcohol 12 (Scheme 2) that is directly oxidized to the corresponding mono-aldehyde and dicarboxylic acid (Scheme 2, 13 and 14). The consecutive Baeyer-Villiger oxidations, ester hydrolyses and alcohol oxidations from the oxo-carboxylic acid intermediate 13 (Scheme 2) also lead to dicarboxylic acids with shorter chains (Scheme 2, 15). In this study on cycloalkenes oxidation, the formate ester 11 has been detected (Table 3, Entry 3) as well as the hydroxy-acid 12 and oxo-acid 13 (Table 1, 2 and 3). In the literature, the formation of intermediates such as 12, 13 and 15 has been detected during alcohols and aldehydes oxidation using H 2 O 2 and phosphotungstic acid. [START_REF] Venturello | [END_REF] In addition to the expected carboxylic acids obtained by oxidation of linear and aromatic aldehydes, the presence of formate esters and their alcohol derivatives has been detected, thus supporting the hypothesis of the implementation of a Baeyer-Villiger oxidation. [START_REF] Venturello | [END_REF] In addition, Venturello and co-workers also described the presence of this side reaction during the oxidative cleavage of 1-methylcyclohexene. Indeed, 5acetoxypentanoic acid was shown to be formed as a byproduct along with the targeted 6-oxoheptanoïc acid.

Thus, the mechanism disclosed in the Scheme 2 for the production of shorter chain diacids confirms the formation of the mono-aldehyde intermediate 9 as a key intermediate in the oxidative cleavage mechanism of cycloalkenes. Finally, this mechanism also explains the formation of shorter chain diacids observed during linear alkene oxidative cleavage, for which formation of aldehyde intermediates is well-established in the literature. 3,4,49 Please do not adjust margins Please do not adjust margins

Conclusions

To summarize, this work proposes a complete mechanism of formation of the products and by-products obtained during the oxidative cleavage of cycloalkenes with H 2 O 2 and H 2 WO 4 . The reaction has been studied with cyclohexene and cyclopentene under various conditions. The structures and proportions of identified by-products were studied from epoxidation/dihydroxylation and oxidative cleavage stages. The present study shows that, along with targeted compounds, dicarboxylic acids shortened by 1 to 3 carbon atoms compared to the expected ones are mainly formed. The production of these by-products is explained by a Baeyer-Villiger oxidation on a mono-aldehyde intermediate that leads to a formate ester, which is hydrolysed and then oxidized to shorter chain diacids. This hypothesis is supported by the identification of formate esters and hydroxyacids but also by results on H 2 O 2 -mediated alcohol and aldehyde oxidation published in the literature, illustrating the formation of a mono-aldehyde intermediate in the cycloalkene oxidative cleavage pathway. The mechanism proposed in this study constitutes a real support for researchers aiming at developing efficient and environmentally-friendly methodologies for the oxidative cleavage of olefins with H 2 O 2 and tungsten-based catalysts. This journal is © The Royal Society of Chemistry 2020

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4 |Please

 4 New J. Chem. 2020, 00, 1-8 This journal is © The Royal Society of Chemistry 2020

Scheme 3 :

 3 Scheme 3: Hypothesis of acid-catalyzed rearrangement of hydroperoxyalcohol intermediate 8 into hydroxy-lactone 5 or mono-aldehyde 9 (adapted from references 29,31,45).

Scheme 4 :

 4 Scheme 4: Competitive oxidation pathways occurring during aldehyde oxidation in the presence of H2O2 and a tungsten-based catalyst. In blue: aldehyde oxidation into carboxylic acid. In red dotted lines: Baeyer-Villiger oxidation (adapted from references 18,45).

Table 1

 1 Oxidative cleavage of cyclohexene in the presence of H2O2, Na2WO4 and Oct3MeN + HSO4 -at different reaction volumes

	Entry a	Reaction volume (mL)	(g) Mass of cyclo-hexene	Conv. b (%)	Yield c (%)	Main by-products (%) d
	1	600	100	100	e	93	e
	2	600	100	100	83
	3	8	1.3	100	47
	4	3	0.5	89		39
	a Experimental conditions: cyclohexene, H2O2 (35%, 4.4 eq.), Na2WO4 (1 mol%), Oct3MeN + HSO4 -(1 mol%), 75-90 °C, 1,000 rpm, 8 h. b Based on the amount of
	converted cyclohexene and calculated by GC with internal standard method.

c

Table 2

 2 Oxidative cleavage of cyclohexene in the presence of different catalytic

	systems
	Entry a	Cat. W	PTC	pH b Conv. c (%)	Yield d (%)	Main by-products (%) e
	1	Na2WO4 . 2H2O	Oct3MeN + HSO4 -	2	100	47 e (4) f
	2	H2WO4	Aliquat 336 ®	3	100	59 e (15) f
	3	H2WO4	Oct3MeN + HSO4 -	< 1	100	45 e (5) f

a Experimental conditions: cyclohexene (16.5 mmol), H2O2 (35%, 4.4 eq.), Cat.W (1 mol%), PTC (1 mol%), 75-90 °C, 1,000 rpm, 8 h. b pH of the aqueous phase during the reaction.

Table 3

 3 Epoxidation of cycloalkenes in the presence of H2O2, H2WO4 and Aliquat 336 ®

	Entry a	Olefin	Temp. (°C)	Conv. b (%)	Yield c (%)	Main-by-products d
	1		25-85	99	89
	2		25-70*	75	0 (39)	e
	3		25-50*	48	3 (32)	e
	a Experimental conditions: cycloalkene (185 mmol), H2O2 (35%, 1.5 eq.), H2WO4 (0.75 mol%), Aliquat 336 ® (0.75 mol%), 25-80 °C, 1,000 rpm, 30 min. b Based on
	the amount of converted cycloalkene and calculated by GC with internal
	standard method

c

Based on the initial amount of cycloalkene and calculated by GC with internal standard method.

d Determined by GC/MS analysis †, yields < 2% e 1,2-cycloalkanediol yield. * Temperature limited by cycloalkene boiling point.

This journal is © The Royal Society of Chemistry 2020New J. Chem., 2020, 00, 1-8 | 3

This journal is © The Royal Society of Chemistry 2020New J. Chem., 2020, 00, 1-8 | 5

Acknowledgements

The authors are grateful to the Région Auvergne Rhône-Alpes for the financial support through an ARC Environnement doctoral research grant (ARC 2016).

Notes and references

Conflicts of interest

There are no conflicts to declare.