Alfredo-Santiago Rodriguez Castillo

Pierre-François Biard
email: pierre-francois.biard@ensc-rennes.fr

Solène Guihéneuf

Ludovic Paquin

Abdeltif Amrane

Annabelle Couvert

Assessment of VOC absorption in hydrophobic ionic liquids: measurement of partition and diffusion coefficients and simulation of a packed column

Keywords: Ionic liquid, volatile organic compound, diffusion coefficient, partition coefficient, absorption, packed column. Highlights

Partition coefficients of toluene and dichloromethane (DCM) in 23 hydrophobic ionic liquids (ILs), which can be used potentially for the physical absorption of volatile organic compounds (VOCs), were measured at 298 K. The partition coefficients, expressed as Henry's law constants, were 400 to 1300 times for toluene and 10 to 47 times for DCM lower in the selected ILs than in water. Thus, the toluene and DCM diffusion coefficients were measured in three high potential hydrophobic ILs and in [Bmim][NTf 2 ] using a thermogravimetric microbalance. Diffusivity measurements were performed at 298K for toluene and between 278 and 308K for DCM. Diffusion coefficients in ILs, ranging between 1 and 4×10 -11 m 2 s -1 , were from 18 to 90 times lower than in water at 298 K. The diffusion coefficients were correlated to the temperature, the solute molar volume, the IL viscosity and molar volume with an average error of 4.2%. Finally, a 3 m industrial packed column was simulated for the removal of DCM and toluene in [AllylEt 2 S][NTf 2 ] and [bmim][NTf 2 ], which both present moderate viscosities of nearly 50 mPa s at 293K. The overall mass-transfer coefficient, the removal efficiency and the pressure drop were calculated and compared to those obtained using other heavy solvents (a silicon

Introduction

Heavy organic solvents such as silicon oils, di-(2-ethylhexyl) adipate (DEHA), phtalates or ionic liquids (ILs) are gaining attention as potential absorbents for the physical scrubbing of hydrophobic volatile organic compounds (VOCs) from gaseous effluents [START_REF] Biard | A simple and timesaving method for the masstransfer assessment of solvents used in physical absorption[END_REF][2][3][4][START_REF] Heymes | A new efficient absorption liquid to treat exhaust air loaded with toluene[END_REF][6][START_REF] Bourgois | Study of mass transfer of VOCs into viscous solvents in a pilot-scale cables-bundle scrubber[END_REF][START_REF] Guihéneuf | Absorption of Hydrophobic Volatile Organic Compounds in Ionic Liquids and Their Biodegradation in Multiphase Systems, Production of Biofuels and Chemicals with Ionic Liquids[END_REF][START_REF] Rodriguez Castillo | Physicochemical properties of some hydrophobic room-temperature ionic liquids applied to volatile organic compounds biodegradation processes[END_REF]. Indeed, besides good absorption capacities for VOCs, these solvents are advantageously characterized by a low or a null vapor tension, a low miscibility in water and good thermal and chemical stabilities. Furthermore, being non-biodegradable and non-toxic, silicon oils and many ILs can be recycled by a biological process [3,[START_REF] Quijano | Absorption and Biodegradation of Hydrophobic Volatile Organic Compounds in Ionic Liquids[END_REF][START_REF] Rodriguez Castillo | Synthesis and toxicity evaluation of hydrophobic ionic liquids for volatile organic compounds biodegradation in a two-phase partitioning bioreactor[END_REF][START_REF] Nguyen | Toluene degradation in a two-phase partitioning bioreactor involving a hydrophobic ionic liquid as a non-aqueous phase liquid[END_REF][START_REF] Rodriguez Castillo | Impact of Activated Sludge Acclimation on the Biodegradation of Toluene Absorbed in a Hydrophobic Ionic Liquid[END_REF][START_REF] Guillerm | Characterization and selection of PDMS solvents for the absorption and biodegradation of hydrophobic VOCs[END_REF].

Ionic liquids are non-flammable molten salts consisting of a large organic cation linked to a counterion typically having a melting point at or below 373 K [START_REF] Welton | Room-temperature ionic liquids: solvents for synthesis and catalysis. 2[END_REF][START_REF] Wilkes | A short history of ionic liquids-from molten salts to neoteric solvents[END_REF][START_REF] Wilkes | Dialkylimidazolium chloroaluminate melts: a new class of room-temperature ionic liquids for electrochemistry, spectroscopy and synthesis[END_REF]. They show many advantages for bioreactor applications as non-aqueous liquid phases according to their tunable related to their wide range of possible structures. Therefore, they can be designed to fulfill the required criteria for hydrophobic VOCs absorption [START_REF] Chiappe | Ionic liquids: solvent properties and organic reactivity[END_REF][START_REF] Huddleston | Characterization and comparison of hydrophilic and hydrophobic room temperature ionic liquids incorporating the imidazolium cation[END_REF][START_REF] Maiti | A correlation-based predictor for pair-association in ionic liquids[END_REF][START_REF] Shkrob | Charge trapping in imidazolium ionic liquids[END_REF][START_REF] Weingärtner | Understanding ionic liquids at the molecular level: facts, problems, and controversies[END_REF] and subsequent biodegradation by a biological material (microorganisms, bacteria, activated sludge, etc.) contained in an aqueous phase in a two-phase partitioning bioreactor [START_REF] Nguyen | Toluene degradation in a two-phase partitioning bioreactor involving a hydrophobic ionic liquid as a non-aqueous phase liquid[END_REF][START_REF] Quijano | Potential of ionic liquids for VOC absorption and biodegradation in multiphase systems[END_REF]. Their high potential for the absorption of different hydrophobic organic compounds has been already demonstrated through the determination of the partition coefficients at infinite dilution (Henry's law constants) of toluene and dimethyldisulfide (DMDS) in two ILs ([Bmim][PF 6 ] and [Bmim][NTf 2 ]) which ranged between 1.5 and 3.2 Pa m 3 mol -1 [START_REF] Quijano | Absorption and Biodegradation of Hydrophobic Volatile Organic Compounds in Ionic Liquids[END_REF]. CO 2 absorption in ionic liquids through partition, and sometimes diffusion coefficients measurement, has also been massively investigated, especially by Shiflett, Yokozeki and their co-workers [START_REF] Shiflett | Separation of N 2 O and CO 2 using roomtemperature ionic liquid [bmim][Ac][END_REF][START_REF] Shiflett | Phase Behavior of N 2 O and CO 2 in Room-Temperature Ionic Liquids[END_REF][START_REF] Shiflett | Separation of N 2 O and CO 2 using room-temperature ionic liquid[END_REF][START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF][START_REF] Shiflett | Solubility of CO 2 in Room Temperature Ionic Liquid[END_REF][START_REF] Yokozeki | Physical and Chemical Absorptions of Carbon Dioxide in Room-Temperature Ionic Liquids[END_REF].

Nonetheless, prospective studies dealing with VOC absorption in ILs are still scarce and focused on toluene, hydrofluorocarbons, alkanes or alkenes [START_REF] Shiflett | Solubility and diffusivity of 1,1,1,2tetrafluoroethane in room-temperature ionic liquids[END_REF][START_REF] Shiflett | Solubility and Diffusivity of Difluoromethane in Room-Temperature Ionic Liquids[END_REF][START_REF] Shiflett | Solubility and diffusivity of hydrofluorocarbons in room-temperature ionic liquids[END_REF][START_REF] Morgan | Diffusivities of Gases in Room-Temperature Ionic Liquids: Data and Correlations Obtained Using a Lag-Time Technique[END_REF][START_REF] Ferguson | Solubility, Diffusivity, and Permeability of Gases in Phosphonium-Based Room Temperature Ionic Liquids: Data and Correlations[END_REF][START_REF] Camper | Diffusion and Solubility Measurements in Room Temperature Ionic Liquids[END_REF].

Two main methods can be used to measure diffusion coefficients of solute/solvent systems. A static configuration (without any gas flow) is recommended to avoid convection contributions [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF]. The thermogravimetric method measures the solute uptake in the investigated solvent by means of a microbalance. Buoyancy corrections must be taken into account in order to correct the expansion of the solvent during the solute absorption [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF][START_REF] Shiflett | Solubility and diffusivity of hydrofluorocarbons in room-temperature ionic liquids[END_REF][START_REF] Jalili | Solubility and diffusion of CO 2 and H 2 S in the ionic liquid 1-ethyl-3-methylimidazolium ethylsulfate[END_REF]. The manometric method measures the pressure decay in a thermo-controlled cell chamber which contains a layer of solvent [START_REF] Camper | Diffusion and Solubility Measurements in Room Temperature Ionic Liquids[END_REF][START_REF] Hou | Experimental Measurement of the Solubility and Diffusivity of CO 2 in Room-Temperature Ionic Liquids Using a Transient Thin-Liquid-Film Method[END_REF].

Nonetheless, these solvents have typically viscosities from 1 to 3 orders of magnitude higher than water, which can alter both their hydrodynamics and mass-transfer performances in usual gas-liquid contactors, especially packed columns which are commonly selected for scrubbing. The lower masstransfer performances observed in viscous solvents are mainly related to lower diffusivities. Indeed, diffusion coefficients 1 or 2 orders of magnitude lower (around 10 -11 m 2 s -1 ) than those encountered in traditional solvents were measured in ILs [START_REF] Ferguson | Solubility, Diffusivity, and Permeability of Gases in Phosphonium-Based Room Temperature Ionic Liquids: Data and Correlations[END_REF][START_REF] Camper | Diffusion and Solubility Measurements in Room Temperature Ionic Liquids[END_REF][START_REF] Condemarin | Gas permeabilities, solubilities, diffusivities, and diffusivity correlations for ammonium-based room temperature ionic liquids with comparison to imidazolium and phosphonium RTIL data[END_REF]. For similar viscosities, diffusivities increase with the molar volume following the order: phosphonium (≈ 600 cm 3 mol -1 ) > ammonium (≈ 400 cm 3 mol -1 ) > imidazolium (≈ 200 cm 3 mol -1 ) demonstrating the influence of the amount of free volume [START_REF] Hou | Experimental Measurement of the Solubility and Diffusivity of CO 2 in Room-Temperature Ionic Liquids Using a Transient Thin-Liquid-Film Method[END_REF][START_REF] Blanchard | High-Pressure Phase Behavior of Ionic Liquid/CO 2 Systems[END_REF][START_REF] Moganty | Diffusivity of Carbon Dioxide in Room-Temperature Ionic Liquids[END_REF]. Conventional correlations usually used to estimate diffusion coefficients (Wilke-Chang, Scheibel, etc.) in traditional solvents have shown high discrepancies for ILs [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF][START_REF] Morgan | Diffusivities of Gases in Room-Temperature Ionic Liquids: Data and Correlations Obtained Using a Lag-Time Technique[END_REF][START_REF] Camper | Diffusion and Solubility Measurements in Room Temperature Ionic Liquids[END_REF][START_REF] Hou | Experimental Measurement of the Solubility and Diffusivity of CO 2 in Room-Temperature Ionic Liquids Using a Transient Thin-Liquid-Film Method[END_REF].

Up to now, the available data about partition and diffusion coefficients of hydrophobic VOCs in a wide selection of ILs specially designed for this application is rather scarce. Furthermore, since the ionic liquids cost is still high, no pilot-plant study has been performed to confirm their potential for VOCs absorption in real gas-liquid contactors such as packed columns. Thus, the aim of this article is to measure the partition and diffusion coefficients of two model hydrophobic VOCs, toluene and dichloromethane (DCM), in an extended panel of 23 ILs presented elsewhere [START_REF] Rodriguez Castillo | Physicochemical properties of some hydrophobic room-temperature ionic liquids applied to volatile organic compounds biodegradation processes[END_REF][START_REF] Rodriguez Castillo | Synthesis and toxicity evaluation of hydrophobic ionic liquids for volatile organic compounds biodegradation in a two-phase partitioning bioreactor[END_REF]. Several cationic scaffolds were explored (imidazolium, isoquinolinium, pyrolidinium, morpholium, triazolium and sulfonium) including functionalized or non-functionalized alkyl side chains and associated with various anions (PF 6 -, NTf 2 -and NfO -). The partition coefficients in these 23 ILs were determined by a static headspace method. Thus, the diffusion coefficients were measured using a thermogravimetric

Material and methods

Chemical products

The 23 ILs investigated were synthesized following a methodology previously described [START_REF] Rodriguez Castillo | Synthesis and toxicity evaluation of hydrophobic ionic liquids for volatile organic compounds biodegradation in a two-phase partitioning bioreactor[END_REF].

Chemical structures and key physical properties were also reported [START_REF] Rodriguez Castillo | Physicochemical properties of some hydrophobic room-temperature ionic liquids applied to volatile organic compounds biodegradation processes[END_REF][START_REF] Rodriguez Castillo | Synthesis and toxicity evaluation of hydrophobic ionic liquids for volatile organic compounds biodegradation in a two-phase partitioning bioreactor[END_REF]. Toluene and dichloromethane (DCM) with a purity higher than 99% were purchased from Acros Organics (Belgium).

Measurement of the partition coefficients at infinite dilution

Presentation of the static headspace method

VOC/IL partition coefficients were deduced from the gas (C G in mol m -3 at 298 K and 1 bar) and liquidphase C L (mol m -3 ) VOC concentrations obtained at the equilibrium in glass vials of 22 mL. The partition coefficients were expressed as K H (Pa m 3 mol -1 ) and K H ' (dimensionless) defined as follows:

K H ' = C G /C L Eq. 1 K H = K H '×R×T Eq. 2
For each VOC/IL systems, six 22 mL vials containing a different initial amount of VOC were prepared by the following procedure. 1 mL of a stock solution of toluene or DCM diluted in IL at 5 µg mL -1 was prepared in a syringe Hamilton AccuDil™ MicroLab®. In parallel, 260 to 460 mL of pure IL were introduced in 22 mL glass vials. These vials were closed with PTFE/silicone septa (Sigma-Aldrich, USA)

and sealed with 20 mm crimp seals. Thus, 40 to 240 mL of the toluene or DCM stock solution were introduced to complete the IL volume at 500 mL in all the bottles. The bottles were maintained under a constant agitation (10 rpm) at 298 K for 72 h using a rotator (Labinco Model L28''TESTTUBE) to reach equilibrium. Then, the headspace VOC concentration (C G ) was quantified by GC-FID and C L was deduced from the mass balance knowing the initial amount of VOC and both the liquid volume and the headspace volume. Control bottles devoid of IL were also monitored in order to ensure gas tightness.

Analytical procedures

The VOC concentration in the gas-phase was quantified by gas chromatography (ThermoScientific-Focus GC, USA). The chromatograph was equipped with a RTX-1 (15 m x 0.32 mmID) column (Restek, USA) and a flame ionization detector. The injector and detector temperatures were maintained at 473 K and 523 K, respectively. For both toluene and DCM, the oven temperature was maintained at 353 K. N 2 was employed as carrier gas at 1.0 mL min -1 . A thermogravimetric microbalance (IGA 003 provided by Hiden Isochema Ltd, Japan) was used to measure the diffusion coefficients. The IGA 003 can operate in both dynamic and static configurations. The main characteristics of this apparatus are presented in the supporting material (Part 1.1) and extensively in the article of Shiflett and Yokozeki [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF]. An enhanced pressured stainless steel (SS316LN) sample container capable of operation from 10 -7 mbar to 10 bar and from 273 to 773 K was installed. Approximately 70 mg of an ionic liquid sample was placed into the sample container and the reactor was then sealed. Samples were dried under deep vacuum (10 -7 mbar) before starting measurements in order to remove any trace of water by following the procedure presented in the supporting material (part 1.2). IGA 003 was operated in a static mode in a pure VOC atmosphere at various pressures. Thus, when the desired temperature was achieved and stable and when the IL sample was completely dried, the admittance and exhaust valves were automatically opened and closed to introduce the VOC gas atmosphere inside the reactor targeting a constant VOC pressure of 50 Pa. The solute uptake in the investigated solvent was registered over time until a plateau corresponding to the thermodynamic equilibrium was reached. Then six additional set-points (at 200, 350, 500, 650, 800 and 950 Pa) were recorded for each solute/IL couples at each temperature. Low pressures were selected in this study to limit the solute mole fraction in the IL (< 6%) to simulate realistic conditions similar of those implemented in an industrial process. Besides, according to [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF], below a 10 % molar fraction, the solute diffusion coefficient in the solvent can be considered at infinite dilution [START_REF] Roustan | Transferts gaz-liquide dans les procédés de traitement des eaux et des effluents gazeux[END_REF]. During each experiment, the sample mass variation allows to determine the mass of solute absorbed in the IL and then the liquid concentration knowing the liquid volume. Buoyancy corrections accounting for gas densities variations with the temperature and pressure have been considered using the procedure of Shifflet and Yokozeki [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF]. The characteristics of the microbalance components and the values of the correction factors used for buoyancy correction are detailed in the supporting material (part 1.3, Tables S.2 and S.3). The pressure ramp was set at 100 mbar min -1 and the temperature ramp was set at 2.0 K min -1 . For each pressure implemented, the plateau was reached in approximately 30-35 hours. To ensure sufficient time for gas-liquid equilibrium, the ionic liquid samples were maintained at the set-point for at least 24h with a maximum time-out of 72h.

Measurement of the diffusion coefficients

Presentation of the method

The influence of the temperature was assessed for DCM from 278. [START_REF] Welton | Room-temperature ionic liquids: solvents for synthesis and catalysis. 2[END_REF]

Mathematical treatment

The breakthrough curves corresponding to the VOC uptake (Fig. 1 and part 1.4 of the supplementary material) where treated using the diffusion model presented by Shiflett and Yokozeki [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF]. The IL initial volume placed in the microbalance vessel was deduced from its dried mass and density at the working temperature. Thus, the initial liquid height (L) was calculated knowing the vessel diameter (80 mm). The model developed by Yokozeki assumed that [START_REF] Yokozeki | Time-dependent behavior of gas absorption in lubricant oil[END_REF]:

 The convective flow was negligible;

 A one-dimensional diffusion process can be considered (z-axis);

 The temperature and pressure inside the reactor remained constant over time;

According to the Fick's law without convection:

Eq. 3

Where C L (mol m -3 ) is the concentration of the solute in the ionic liquid, t (s) is the time, z (m) is the vertical coordinate and D i is the diffusion coefficient (m 2 s -1 ). The initial and boundary conditions were:

C L = C L,0 when t = 0 and 0 < z < L Eq. 4 C = C L,S when t > 0 and z = 0 Eq. 5 at z = L Eq. 6

L (m) is the depth of the ionic liquid in the vessel, z = 0 corresponds to the vapor-liquid boundary, C L,0

is the known initial homogeneous solute concentration and C L,S is the solute saturation concentration (mol m -3 ). The VOC concentration in the IL at any time (C) can be deduced from the following analytical solution:

Eq. 7

Where

Few iterations (n =15) were necessary to get the convergence. A non-linear regression was performed to determine D i for each experiment trying to minimize the least squares objective function between the measured values of C L and those deduced from Eq. 7 using the Excel Solver (time max = 100 s, iteration = 1000, precision 10 -7 , tolerance = 1%, convergence = 10 -5 , quadratic estimations, central derivation and conjugated gradient method). * AR is the affinity ratio defined as K H in water divided by K H in IL.

Results and discussion

Determination of the VOC/IL partition coefficients

† At 298 K according to [3].

The VOC/ILs partition coefficients at infinite dilution were measured by the static headspace method using six vials prepared with different initial amount of VOC. At the equilibrium, the gas concentration was proportional to the liquid concentration according to the Henry's law with determination coefficient from 98.8% to 99.95%. Thus, the dimensionless partition coefficients (K´H)

were deduced from the slope of the linear regression between C G vs C L (Table 1). The results show that toluene partition coefficients in hydrophobic ILs were roughly in the range 0.5-4 Pa m 2013) can be justified by the fact that they used a dynamic method in which aerodynamic drag forces can biased the results {Bedia} [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF]. For the system toluene/[Bmim][PF 6 ], the partition coefficient was 1.6 % higher than the value reported by Quijano et al. [START_REF] Quijano | Potential of ionic liquids for VOC absorption and biodegradation in multiphase systems[END_REF]. Being less hydrophobic than toluene and without potential  interactions, the DCM partition coefficients were from 1.67 to 30 times higher than the toluene partition coefficients, in the range from 5 to 17 Pa m 3 mol -1 , but they remain significantly lower than in water (from 14 to 50 times). The toluene partition coefficients in the ionic liquids are close to those determined in other heavy solvents such as DEHA and silicon oils. However, the DCM partition coefficients in ionic liquids are in many cases higher than the one measured in DEHA (4.73 Pa m 3 mol -1 at 293K) and close to the one in a silicon oil, namely polydimethylsiloxane (PDMS) 50 [START_REF] Biard | A simple and timesaving method for the masstransfer assessment of solvents used in physical absorption[END_REF].

Both the anion nature and cation structure strongly influence the toluene and DCM partition coefficients, sometimes with similar effects and sometimes with adverse effects (Table 2). These results suggest that the IL selection for a practical application containing a mixture of different VOCs should not be based on the determination of only one partition coefficient with a model VOC, such as toluene which has been often considered in previous studies. The worst affinities are obtained with the NfO -anion, whereas Ntf 2 -and PF 6 -anions are respectively the most interesting for toluene and DCM. For both DCM and toluene, the best affinities are observed with the isoquinolium cation and the worst affinities with the triazolium and pyridinium-based ionic liquids, showing that the affinities are directly related to the size core, and thus intermolecular and electrostatic forces. As expected, a modification of the structure of the alkyl chain of the cation significantly influences the partition coefficients as it is summarized in Table 2.

Table 2. Comparison of the influence of the anion nature and cation structure of the IL on the toluene and DCM affinities.

Parameter Influence on the toluene affinity Influence on the DCM affinity Influence of the anion ] as a model IL commonly described in the literature, and these three ILs were selected for diffusion coefficients measurement.

[NTf 2 ] > * [PF 6 ] > [NfO] [PF 6 ] > [NTf 2 ] > [NfO] Influence of the cation core [Iq] > [Morph] > [Triaz] > [im] > [Pyrr] [Iq] > [Morph] > [im] > [Triaz] > [Pyrr] -C=C

Diffusion coefficients measurement

Results

Toluene diffusion coefficients at 298 K were measured in the four selected ILs to assess the influence of their properties. The influence of the temperature was assessed with the DCM/[OctIq][NTf 2 ] * > means "better than" † + (-) means that this factor positively (negatively) influences the affinity with lower (higher) partition coefficients.

system. All the breakthrough curves corresponding to the solute uptakes are presented as supplementary material (Figs S1-S8). At a given temperature, the pressure had no significant influence on the diffusion coefficient between 200 Pa and 950 Pa (Tables S. 4 and S.5). It validates the assumption of an infinite dilution for a VOC mole fraction lower than 10%; otherwise, the diffusion coefficients would have been correlated to the mole fraction and the pressure. The average diffusion coefficients at each temperature are therefore summarized in Table 3. On the one hand, the significant dispersion of the data at different pressures (with relative standard deviations RSD from 4 to 17%) is justified by the experimental uncertainties and the low sensitivity of the mass-transfer rate to the diffusion coefficient. Indeed, Fig. 2, which simulates breakthrough curves for over and underestimated diffusion coefficients by 20%, shows a limited influence. On the other hand, this uncertainty has a limited impact on practical applications since the mass-transfer rate and the gasliquid contactor design have a limited sensitivity to the liquid diffusion coefficient (part 3.3.5 and [START_REF] Biard | Volatile organic compounds absorption in packed column: theoretical assessment of water, DEHA and PDMS 50 as absorbents[END_REF]). The determined toluene diffusivity in [Bmim][NTf 2 ] at 298 K was 81% lower than the value found by Bedia et al. who used a not recommended dynamic method [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF][START_REF] Bedia | Optimized ionic liquids for toluene absorption[END_REF].

Correlation between diffusion coefficients, temperature and physicochemical properties

Tyn and Calus

Where

Hayduk and Minhas

Siddiqi and Lucas

Several theoretical and semi-empirical correlations (Table 4) predict that diffusion coefficients are inversely proportional to the solvent viscosity. The viscosities of the selected ILs are from 50 to more than 600 times higher (Table 5) than the water viscosity but the measured diffusion coefficients are only from 18 to 90 times lower than in water at 298K. It shows that the large viscosities are partly * V m,i is the molar volume of the species i (VOC or solvent) in cm 3 mol -1 , m L is the solvent viscosity in mPa s -1 , Pa is the parachor of the species i in g 0.25 cm 3 mol -1 s -0.5 , T is in K, A i,  and C are dimensionless constants.

compensated by higher molar volumes (roughly 10 to 20 times higher than water). Besides, according to all these theories, the diffusion coefficient is proportional to the temperature and decrease with the solute molar volume with different significances. ) m L (mPa s) r L (kg m -3 ) s L (mN m -1 ) V m,L (cm 3 mol -1 ) The measured diffusion coefficients were compared to those calculated from the correlations listed in Table 4. The molar volumes of the solvents at their boiling point, which were unknown, were required. Therefore, the molar volumes were calculated at the working temperature. The results are summarized in the supplementary material (Tables S. 6 and S.7). In agreement with the observations of other studies [27, 33-35, 43, 45, 47], these correlations developed for conventional solvents poorly fit the diffusion coefficients in heavy solvents. Indeed, the average absolute relative error ranged from 21 to 65% for the toluene diffusion coefficients (with relative error either positive or negative) and from 61 to 91 % (with only negative relative error) for the DCM diffusion coefficients (Tables S.8

[
and S.9). Since the correlations of Wilke-Chang, Scheibel and Arnold contain empirical fitting variables (, C, A VOC A L , Table 4), these ones were optimized to minimize the least square objective function between the calculated and measured diffusion coefficients (Tables S.10 and S.11). Reliable values of , C and A VOC A L close to the initial values were obtained (Table 4). However, this procedure did not allow to significantly improve the accuracy of the predictions. These discrepancies emphasize that the correlations of the literature poorly correlate the diffusion coefficients in ILs to the various influential parameters (temperature T, solute and solvents molar volume V m,VOC and V m,L , solvent viscosity m L ). Thus, a power-law function similar to the equation of Siddiqi-Lucas, was developed trying to minimize the least square objective function between the model and the experimental diffusion coefficients:

Eq. 8

Where the diffusivity (D i ) is in m 2 s -1 , the viscosity µ L is in mPa s and the molar volumes V m are in cm 3 mol -1 . The average relative error of 4.2% between the model and the experimental diffusivities is particularly low (Table 3). Furthermore, the CO 2 diffusion coefficients in [bmim][PF 6 ] extrapolated from this correlation (taking a CO 2 molar volume of 55 cm 3 mol -1 [START_REF] Camper | Diffusion and Solubility Measurements in Room Temperature Ionic Liquids[END_REF]), were very close to those found by Shifflet and Yokozeki (2005), in the range 8-30% for a temperature from 283.15 to 348.15 K [START_REF] Shiflett | Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids[END_REF].

On the one hand, the developed correlation presents a higher sensitivity to the temperature than the correlations listed Table 4, with a corresponding power of 1.63. This trend is in agreement with the observations of [START_REF] Morgan | Diffusivities of Gases in Room-Temperature Ionic Liquids: Data and Correlations Obtained Using a Lag-Time Technique[END_REF], which support a much larger temperature effect for diffusion in ionic liquids [START_REF] Morgan | Diffusivities of Gases in Room-Temperature Ionic Liquids: Data and Correlations Obtained Using a Lag-Time Technique[END_REF]. Besides, Hou and Baltus found that the diffusivity of CO 2 in several ionic liquids varies with the temperature with a power of 3.3 [START_REF] Hou | Experimental Measurement of the Solubility and Diffusivity of CO 2 in Room-Temperature Ionic Liquids Using a Transient Thin-Liquid-Film Method[END_REF]. On the other hand, diffusivity appears to vary inversely with the viscosity to the power of 0.702. Therefore, the diffusivity in IL seems advantageously less sensitive to the viscosity than the other correlations currently used for traditional solvents. Scovazzo and his co-workers found similar values (0.66 for the imidazolium, 0.34-0.47 for phosphonium, and 0.59 for the ammonium based ILs) investigating the diffusion of ethylene, propylene, 1-butene, butadiene, methane and butane in several ionic liquids [START_REF] Morgan | Diffusivities of Gases in Room-Temperature Ionic Liquids: Data and Correlations Obtained Using a Lag-Time Technique[END_REF][START_REF] Ferguson | Solubility, Diffusivity, and Permeability of Gases in Phosphonium-Based Room Temperature Ionic Liquids: Data and Correlations[END_REF][START_REF] Condemarin | Gas permeabilities, solubilities, diffusivities, and diffusivity correlations for ammonium-based room temperature ionic liquids with comparison to imidazolium and phosphonium RTIL data[END_REF].

All these results showed that to maximize the solute diffusivities, pure ILs or mixture with moderate viscosities and high molar volume (and high molar mass) should be developed. Indeed, a flexible structure combined to a high molar volume in order to increase voids within the ionic liquid, such as in phosphonium-based ionic liquids, allow to enhance solute diffusion [START_REF] Morgan | Diffusivities of Gases in Room-Temperature Ionic Liquids: Data and Correlations Obtained Using a Lag-Time Technique[END_REF][START_REF] Skrzypczak | Diffusion-Controlled Electron-Transfer Reactions in Ionic Liquids[END_REF].

Assessment of ionic liquids for VOC removal

Introduction

On the one hand, VOC partition coefficient measurements (part 3.1) undoubtedly emphasize the high potential of ionic liquids for hydrophobic VOC absorption with toluene partition coefficients from 200 to 1400 times lower than in water and with DCM partition coefficients from 14 to 50 times lower than in water. On the other hand, VOC diffusion coefficients in the selected ionic liquids (part 3.2) are from 18 to 90% lower than in traditional solvents such as water at 298 K. Consequently, ionic liquids present a high absorption capacity for hydrophobic VOCs but their high viscosity might limit the mass-transfer rate in a gas-liquid contactor. Up to now, no experimental work has been performed using ionic liquids on a realistic gas-liquid contactor such as a counter-current packed column since the synthesis of massive amounts of ionic liquid is still challenging. However, the prediction of the

Theoretical background

T (K) F G (Nm 3 h -1
)

F L (m 3 h -1
) 6) and packing characteristics (Table S.12) than in the article of [START_REF] Biard | Volatile organic compounds absorption in packed column: theoretical assessment of water, DEHA and PDMS 50 as absorbents[END_REF] were considered in order to compare the results to DEHA and PDMS 50 [START_REF] Biard | Volatile organic compounds absorption in packed column: theoretical assessment of water, DEHA and PDMS 50 as absorbents[END_REF]. The removal efficiency, defined by Eq. 9, was considered as the main performance indicator to assess the potential of the solvents along with the pressure drop:

L/G U SG (m s

Eq. 9

Where C G,i and C G,o are the VOC concentrations in the gas at respectively the inlet and the outlet of the packing. Assuming isothermal liquid and gas plug flows at counter-current, the removal efficiency Eq. 11 K L a° is the overall volumetric liquid-phase mass-transfer coefficient (s -1 ) which is related to the gas and liquid-side coefficients (k G and k L in m s -1 ), the interfacial area (a° in s -1 ) and the Henry's law constant (K H in Pa m 3 mol -1 ) :

Eq. 12

The determination of the loading and flooding points, between which the systems should be operated, of the interfacial area (a°) and of the liquid hold-up (h L ) is necessary prior to calculate K L a°.

The dedicated correlations of Billet-Schultes, which have been developed with solvents having kinematic viscosities (m L /r L ) up to 100 or 142×10 -6 m 2 s -1 (depending on the determined variable),

Simulation of the hydrodynamics

Owing to similar viscosities, surface tensions and densities (Table 5), the hydrodynamics parameters simulated for the two ILs were particularly close (Table 7). The loading (U SG,lo ) and flooding (U SG,fl )

velocities are advantageously higher in the two considered ionic liquids (respectively around 1.3 and 2.4 m s -1 ) than in DEHA and PDMS 50, even with similar viscosities. This behavior is supported by the fact that the high viscosity of these two ILs is counterbalanced by a high density (around 50% higher than PDMS 50 and DEHA). A liquid hold-up (h L ) of nearly 14-15%, similar to those simulated for DEHA and PDMS 50, were calculated. Finally, an acceptable pressure drop of nearly 400 Pa m -1 , around 40% higher than in water, was simulated [START_REF] Biard | Volatile organic compounds absorption in packed column: theoretical assessment of water, DEHA and PDMS 50 as absorbents[END_REF].

In agreement with the results published earlier considering DEHA and PDMS 50 [START_REF] Biard | Volatile organic compounds absorption in packed column: theoretical assessment of water, DEHA and PDMS 50 as absorbents[END_REF], the interfacial areas simulated using the B-S theory were particularly large (≈ 340 m 2 m -3 ) and 244% higher than the packing specific surface (A p = 139 m 2 m -3 ) which seems unlikely. Such a high discrepancy is not surprising since this correlation was essentially developed with water-like systems with kinematic viscosities in the range 0.14-1.66 m 2 s -1 , which is far to include heavy solvents [START_REF] Billet | Prediction of mass transfer columns with dumped and arranged packings: updated summary of the calculation method of Billet and Schultes[END_REF][START_REF] Billet | Predicting mass transfer in packed columns[END_REF]. Recently, Song-Seibert-Rochelle proposed a new correlation to calculate a° using random and structured packings for viscous solvents up to 70 mPa s [START_REF] Song | Mass Transfer Parameters for Packings: Effect of Viscosity[END_REF][START_REF] Song | Effect of Liquid Viscosity on Liquid Film Mass Transfer for Packings[END_REF] :

Eq. 13
With for a metal random packing operated in the loading zone.

This correlation does not depend on the viscosity since the authors concluded that it does not have a significant effect on a°. It leads to a value of a° 37% higher than A p , which is more realistic than using the B-S theory. The experimental observations of S-S-R support the fact that a° might be higher than A p since the liquid can flow as large rivulets, droplets and waves and practically stagnant liquid might be present within the column [START_REF] Song | Effect of Liquid Viscosity on Liquid Film Mass Transfer for Packings[END_REF].

The interfacial area found using the S-S-R theory was compared to the values deduced from the Piché et al. and Onda correlations, which were both developed with water-like systems [START_REF] Biard | Volatile organic compounds absorption in packed column: theoretical assessment of water, DEHA and PDMS 50 as absorbents[END_REF][START_REF] Piché | Interfacial mass transfer in randomly packed towers: a confident correlation for environmental applications[END_REF][START_REF] Onda | Mass transfer coefficients between gas and liquid phases in packed columns[END_REF].

These two theories predicted realistic but low interfacial areas, which do not support the observations of S-S-R. Consequently, only the values of a° deduced from Eq. 13 was considered to calculate the overall volumetric liquid-phase mass-transfer coefficient from Eq. 12 in the section 3.3.4.

Table 7: Determination of the loading and flooding points, liquid hold-up, linear pressure drop by the B-S theory and of the interfacial area by several theories.

Solvent U SG,lo

)

U SG,fl (m s -1
)

U SG /U SG,fl h L (%) P/z (Pa m -1 ) a° (m 2 m -3 ) Piché

Simulation of the mass-transfer and calculation of the removal efficiency

Both the S-S-R and B-S theories were considered to calculate the liquid and gas-film mass-transfer coefficients (k L and k G ). Since the gas-film mass-transfer coefficients is not affected by the liquid properties, realistic and rather close values of k G , in the range 2.3-4.3×10 -2 m s -1 , were deduced considering both theories (Tables 8 and9). The values of k G determined with the B-S correlation were from 50 to 60% higher than those determined with the S-S-R correlation. This slight discrepancy has a low influence on the removal efficiency calculation since it has a low sensitivity to k G (part 3.3.5).

However, the two theories present high discrepancies for the calculation of k L . Indeed, the B-S theory predicted values of k L around 8 times higher than the S-S-R theory (Tables 8 and9). On the one hand, according to the B-S theory, k L does not depend directly on the viscosity and surface tension but depends on them indirectly through their influence on the diffusivity (with a power of ½ according to the penetration theory) and liquid hold-up (with a power of -½) which varies only from a factor 3 between heavy solvents and water (Table 7) [START_REF] Biard | A simple and timesaving method for the masstransfer assessment of solvents used in physical absorption[END_REF]. On the other hand, the S-S-R theory predicts a total dependence of k L on the viscosity with a power of -0.75, of which -0.35 is from the indirect influence through diffusivity, and -0.4 is from the direct influence through liquid turbulence [START_REF] Song | Effect of Liquid Viscosity on Liquid Film Mass Transfer for Packings[END_REF]. Thus, the higher sensitivity of the S-S-R correlation to the viscosity leads to very low and probably underestimated values of k L . Thus, the experimental values of K L a° determined by Guillerm et al.

(2016) for the toluene absorption in PDMS 50 using two different packings (one random packing:

IMTP and one structured packing: Flexipac) were compared to the values deduced using the correlations of S-S-R [START_REF] Guillerm | Absorption of toluene in silicone oil: effect of the solvent viscosity on hydrodynamics and mass transfer[END_REF]. The experimental values were in average 17% (IMTP packing) and 53%

(Flexipac packing) higher, confirming the tendency of the correlations of S-S-R to underestimate k L and K L a° (Fig. S9). Thus, as an alternative, a combination of the S-S-R theory, to calculate a°, and of 8 and9). This combination leads to K L a° values around 80% higher than those deduced considering only the S-S-R theory, which might be rather optimistic regarding the relative difference between the experimental results of Guillerm et al.

(2016) and the correlations of S-S-R [START_REF] Guillerm | Absorption of toluene in silicone oil: effect of the solvent viscosity on hydrodynamics and mass transfer[END_REF]. Thus, the real values of K L a° (and of HTU and Eff) should be included with a good confidence level between these two predictions. From the K L a° values, the heights of a transfer unit and the removal efficiencies were calculated using Eq. 10. Fig. S10 shows a comparison between the experimental values of Eff measured by [START_REF] Guillerm | Absorption of toluene in silicone oil: effect of the solvent viscosity on hydrodynamics and mass transfer[END_REF] and those deduced considering only the S-S-R theory. The experimental values were in average 11% (IMTP packing) and 23% (Flexipac packing) higher than the theoretical one. The results published previously for DEHA and PDMS 50 were updated with the S-S-R theory, with interfacial areas of 180 and 192 m 2 m -3 , respectively (Table 7) [START_REF] Biard | Volatile organic compounds absorption in packed column: theoretical assessment of water, DEHA and PDMS 50 as absorbents[END_REF]. The resulting removal efficiencies are provided Fig. 2 for comparison with the two simulated ILs. The toluene removal efficiency was higher in DEHA than in PDMS 50 and the two ILS and should be in the range 99.6%-99.97% depending on the considered correlations used to determine the mass-transfer coefficients. This result is mainly due to a lower toluene partition coefficient in DEHA (0.76 Pa m 3 mol -1 ) than in the other solvents and with a lower extent to a lower viscosity leading to higher diffusion coefficients. PDMS 50 and [AllylEt 2 S][NTf 2 ] exhibited similar interesting performances whatever the considered theory (99.6%

with the S-S-R/B-S theories combination, 72% with the S-S-R theory). Eff in [bmim][NTf 2 ] was lower than in the other solvents owing to a higher partition coefficient (1.44 Pa m 3 mol -1 ) and a lower diffusion coefficient than in PDMS 50, but it remains competitive (97.6% with the S-S-R/B-S combination, 53% with the S-S-R theory). The DCM simulated removal efficiencies were more disappointing, in agreement with significantly higher partition coefficients. Indeed, whatever the theory considered, the silicon oil and both ILs exhibited removal efficiencies lower than 40%, emphasizing the higher potential of DEHA to remove a large panel of VOCs [START_REF] Biard | A simple and timesaving method for the masstransfer assessment of solvents used in physical absorption[END_REF].

Sensitivity analysis

Fig. 2 emphasizes a rather high discrepancy between the two considered theories. Nonetheless, it should allow to assess the potential of a heavy solvents to remove a given VOC with a rather good confidence level since Eff might be more affected by K H than by K L a° (and consequently by the liquidphase diffusion coefficient). To confirm this, a sensitivity analysis based on the determination of the elasticity index (EI) was carried out [START_REF] Dang | Assessment of a Stirred-Cell Reactor Operated Semicontinuously for the Kinetic Study of Fast Direct Ozonation Reactions by Reactive Absorption[END_REF]. The selected output was the removal efficiency and the inputs were k L , k G , K L a° and K H . EI were calculated for the four studied VOC/ILs systems simulated.

The results confirm undoubtedly the low sensitivity of Eff to k G , the mass-transfer resistance being predominantly located in the liquid phase. The sensitivity to k L was moderate, especially for toluene with EI lower than 0.3, which means that an uncertainty on k L of 10% will affect Eff by less than 3%.

Then, since k L increases with D L at the power of 0.5, the EI values for D L are 2.6 times lower than the one for k L , showing a limited sensitivity of k L to D L . The sensitivity to a° (K L a°) was higher but this parameter was determined with a better confidence level than k L , whose the value can vary on several orders of magnitude (0.1 to 50×10 -4 m s -1 for k L for example). Finally, the results confirmed the higher sensitivity of Eff to the partition coefficient K H , especially for DCM. Since K H values were determined accurately, it confirms that the assessment of different solvents through the determination of the partition coefficient is rather pertinent and that the simulations carried out allows comparing different solvents with a good confidence level.

k L k G K L a°K H k L k G K L a°K H [AllylEt 2 S][NTf 2 ] [bmim][NTf 2 ]

Conclusion

Partition coefficient of toluene and DCM in 23 hydrophobic ILs were measured by the static headspace method at 298K. The results clearly demonstrated the high affinity of ionic liquids for hydrophobic VOCs, especially toluene. The diffusion coefficients at infinite dilution were also measured using a thermogravimetric microbalance for four selected ionic liquids. These diffusion coefficients ranged between 1 and 4×10 -11 m 2 s -1 for temperature in the range 278-308 K and were from 18 to 90 times lower than in water. The diffusion coefficients were satisfactorily correlated to the temperature, the solvent viscosity and both solvent and solute molar volumes, with an average relative error of 4.2%. The correlation highlighted advantageously a stronger dependence of the diffusion coefficient to the temperature and a lower dependence to the solvent viscosity than the conventional correlations. The hydrodynamics of a counter-current packed column fed with (2.45 times higher than the packing specific surface area). Thus, a combination of these two theories was proposed to determine the overall liquid-side mass-transfer coefficients. The results emphasized the good potential of the two ILs for the toluene absorption. However, the DCM removal efficiencies were quite disappointing, between 14% and 44%, higher than in PDMS 50 but significantly lower than

  balance in [Bmim][NTf 2 ] as a reference IL widely studied in the literature and in three pertinent ionic liquids ([Bmim][PF 6 ], [OctIq][NTf 2 ] and [AllylEt 2 S][NTf 2 ]). Experimental diffusion coefficients were compared to those deduced by conventional correlations and a new correlation was presented. Finally, the hydrodynamics and mass-transfer in a packed column fed with [Bmim][NTf 2 ] and [AllylEt 2 S][NTf 2 ] were simulated for DCM and toluene absorption.

Figure 1 .

 1 Figure 1. Example of a static absorption experiment and analysis of the toluene uptake sensitivity to the diffusion coefficient. The determined diffusion coefficient was over and underestimated by 20% ([OctIq][NTf 2 ] at 350 Pa and at 298 K).

  hydrodynamics and mass-transfer rate in a packed column considering ionic liquids with moderate viscosities, such as [AllylEt 2 S][NTf 2 ] and [Bmim][NTf 2 ], is possible since theirs viscosities match the range covered by a few theories developed for viscous solvents.

  packed column (1.0 m of internal diameter and 3.0 m of height), consisting of 35 mm metal Pall rings, was simulated for the DCM and toluene absorption at counter-current in [AllylEt 2 S][NTf 2 ] and [Bmim][NTf 2 ]. The same operating conditions (Table

(

  Eff) obtained for a given column height (Z in m) is deduced by the following equation which does not depend on C G,i [41]: with and Eq. 10 NTU OL (no unit) and HTU OL (m) are respectively the overall Number and Height of a Transfer Unit in the liquid phase. F L is the liquid flow-rate (m 3 s -1 ), S col is the column diameter (m 2 ) and A is the absorption rate (dimensionless):

include [AllylEt 2 S

 2 ][NTf 2 ] and [Bmim][NTf 2 ] [44, 49-52]. For the determination of the mass-transfer coefficients and of the interfacial area, both the correlations of Billet-Schultes (B-S) and the recent correlation of Song-Seibert-Rochelle (S-S-R), specially designed for viscous solvents up to 70 mPa s, were essentially considered [52-55].

  the B-S theory, to calculate both k L and k G , was considered for the simulation of the VOCs masstransfer in [AllylEt 2 S][NTf 2 ] and [Bmim][NTf 2 ] (Tables

Figure 2 .

 2 Figure 2. Toluene (a) and DCM (b) removal efficiencies simulated in various heavy solvents according to the operating conditions selected (Table 6). Blue bars : k L and k G are deduced from the B-S theory and a° is deduced from the S-S-R theory; green bars : k L , k G and a° are deduced from only the S-S-R theory.

  /S-S-R theories combination S-S-R theory (b)

Figure 3 .

 3 Figure 3. Elasticity index calculated for toluene (a) and DCM (b). Output: removal efficiency, Inputs : k L , k G , K L a° and Eff. The BS/S-S-R theories combination was considered.

[

  bmim][NTf 2 ] and [AllylEt 2 S][NTf 2 ] at 293 K was simulated considering the Billet-Schultes theory.Realistic and worthwhile loading and flooding velocities (respectively around 1.3 and 2.4 m s -1 ) were determined despite the high IL viscosity, which was partly compensated by their high density. The linear pressure drop calculated, around 400 Pa m -1 , was competitive and comparable to those simulated with DEHA and PDMS 50. Then, the overall liquid-side mass-transfer coefficients were calculated considering both the Billet-Schultes and Song-Seibert-Rochelle correlations to finally determine the removal efficiency in a 3 m height column. The S-S-T theory predicted reliable interfacial areas, but low and unlikely liquid-film mass-transfer coefficients (in the range 0.15-0.25×10 -5 m s -1 ), whereas the B-S theory predicted reliable values of the liquid-film mass-transfer coefficient (in the range 1.1-1.9×10 -5 m s -1 ) but very high and unlikely values of the interfacial area

Glossarya°:

  interfacial area relative to the packing volume (m 2 m -3 ) A: absorption rate (dimensionless) A i : abnormality factor to account of system non-idealities (Arnold correlation) A p : packing specific surface area (m 2 m -3 ) AR: affinity ratio defined as K H in water divided by K H in IL B-S: Billet-Schultes C: Constant (Scheibel correlation or Eq.12) C L or (C G ): VOC concentration in the liquid phase (gas phase, mol m -3 or mol L -1 ) d p : packing size (m) DCM: dichloromethane D col : column diameter (m) D i or D L : diffusion coefficient at infinite dilution of a solute i in the liquid phase (m 2 s -1 ) D G : diffusion coefficient at infinite dilution of a solute in the gas phase (liquid phase) (m 2 s -1 ) Eff: removal efficiency EI: elasticity index F: flow-rate (m 3 s -1 or L s -1 , often expressed in the normal conditions of temperature and pressure for a gas) g: acceleration of gravity (9.81 m s -2 ) T: temperature of the contactor (K) t: time (s) U: fluid velocity (m s -1 ) V m : solute or solvent molar volume (cm 3 mol -1 ) VOC: volatile organic compound Z: contactor height (m) z: vertical coordinate (m) Greek letters:  Association factor (Wilke-Chang correlation) : void fraction (%) P/z: linear pressure drop (Pa) m: dynamic viscosity (Pa s) s: surface tension (N m -1 ) r: density (kg m -3 ) Subscripts: fl: at the flooding point G: relative to the gas L: relative to the liquid (solvent) lo: at the loading point O: overall o: at the packing outlet p: relative to the packing S: superficial (velocity) s: final VOC: relative to the VOC (solute) 0: initial

Table 1 . Toluene and DCM partition coefficients measured at 298K. The determination coefficient (R 2 ) corresponds to the linear regression between C G vs C L based on six points corresponding to six vials with different initial amounts of VOC. Data in bold correspond to the four ILs selected for diffusion coefficient measurements (Part 3.2).

 1

				Toluene				Dichloromethane
		VOC	K H Pa m 3 mol -1	10 4 ×K´H	R % 2	AR	*	K H Pa m 3 mol -1	10	4 ×K´H	2 % R	AR
	Water	†	677	2.73×10 3	-	1		243	9.79x10	3	-	1
	[Bmim][NTf 2 ]	1.44	5.81	99.86 470	11.58	46.71	99.46 21.0
	[Bmim][PF 6 ]	2.42	9.76	99.79 280	10.46	42.26	99.74 23.2
	[Bmim][NfO]	2.81	11.35	99.62 241	13.96	56.32	98.83 17.4
	[nPrmim][NTf 2 ]	0.73	2.95	99.58 927	12.46	50.26	99.97 19.5
	[iPentmim][PF 6 ]	2.56	10.31	99.77 264	10.70	43.15	99.70 22.7
	[iPentmim][NTf 2 ]	0.63	2.54	99.58 1075	11.15	44.99	99.74 21.8
	[Butenylmim][PF 6 ]	3.66	14.77	99.43 185	9.96	43.31	99.60 24.4
	[Butenylmim][NTf 2 ]	1.91	7.71	99.67 354	12.00	48.41	99.94 20.3
	[Butenylmim][NfO]	3.13	12.62	99.96 216	5.23	21.09	99.95 46.5
	[MeOEmim][NTf 2 ]	1.92	7.75	99.89 353	15.52	62.59	99.67 15.7
	[EtOEmim][NTf 2 ]	1.66	6.70	99.20 408	12.28	49.54	99.86 19.8
	[MeOEOEmim][NTf 2 ]	2.02	8.16	99.58 335	12.97	52.34	99.78 18.7
	[MeOEmim][NfO]	0.78	3.16	99.91 868		Undetermined
	[

OctIq][NTf 2 ] 0.50 2.01 99.93 1354 9.96 40.16 99.57 24.4

	[DecIq][NTf 2 ]	0.52	2.11	99.93 1302	5.09	20.52	99.84 47.7
	[MeOEIq][NTf 2 ]	1.37	5.54	98.21 494	12.45	50.23	99.55 19.5
	[EtOEIq][NTf 2 ]	0.53	2.12	99.74 1277	12.27	49.51	99.68 19.8
	[CNC 3 mim][NTf2]	3.12	12.60	99.87 217	15.48	62.44	99.71 15.7
	[BMTriaz][NTf 2 ]	0.95	3.84	99.73 713	14.13	56.99	99.72 17.2
	[CF 3 CF 2 BTriaz][NTf 2 ]	0.57	2.31	99.09 1188	17.00	68.60	99.51 14.3
	[BMPyrr][NTf 2 ]	1.76	7.10	99.78 385	10.51	42.41	99.88 23.1
	[AllylEt 2 S][NTf 2 ]	0.88	3.56	99.73 769	12.18	49.14	99.93 20.0
	[MeOEMMorph][NTf 2 ]	0.75	3.01	99.48 903	9.35	37.72	99.30 26.0
	[EtOEMMorph][NTf 2 ]	0.81	3.25	99.14 836	16.92	68.25	99.40 14.4

  3 mol -1 (from 200 to 1400 times lower than in water) and are particularly competitive. These results are supported by the fact that toluene is very hydrophobic (octanol-water partition coefficient of 2.73)

and can involve potential -stacking interactions with ionic liquids. The measured partition coefficient for the system toluene/[Bmim][NTf 2 ] was 5.0% lower than the value reported by Quijano et al. and 2.5 times higher than the value reported by Bedia et al.

[START_REF] Quijano | Potential of ionic liquids for VOC absorption and biodegradation in multiphase systems[END_REF][START_REF] Bedia | Optimized ionic liquids for toluene absorption[END_REF]

. The quite high discrepancy observed with

Bedia et al. (

Table 3 . Average diffusion coefficients measured. The raw results at different pressures are listed on Tables S.4 and S.5. RE corresponds to the relative error between the modeled and experimental diffusion coefficients. Experimental Model (Eq. 8)

 3

	VOC		IL	T (K)	10 11 ×D i (m 2 s -1 )	RSD (%)	10 11 ×D i (m 2 s -1 )	* RE (%)
				[OctIq][NTf 2 ]	298.15 0.98±0.17	17	0.965	-1.54
	Toluene	†	[Bmim][NTf 2 ] [Bmim][PF 6 ]	298.15 3.42±0.48 298.15 1.33±0.26	14 27	4.01 1.32	+17.2 -0.79
				[AllylEt 2 S][NTf 2 ] 298.15 4.86±0.92	19	4.34	-10.7
					278.15 0.88±0.06	7	0.876	-0.42
	DCM	‡		[OctIq][NTf 2 ]	288.15 1.53±0.15 298.15 2.53±0.28	10 11	1.51 2.51	-1.46 -0.93
					308.15 4.06±0.17	4	4.04	+0.50
	-11 m 2 s -1 in water at 298K [1]. -11 m ‡ D DCM = 127×10 2 s

* Average relative error of 4.2%.

† D toluene = 89.0×10 -1 in water at 298K

[START_REF] Biard | A simple and timesaving method for the masstransfer assessment of solvents used in physical absorption[END_REF]

.

Table 4 . Correlations for diffusion coefficient calculation. Adapted from [33, 45, 46].

 4

	Stoke-Einstein	with r VOC the radius of the VOC molecule
	Wilke-Chang
		 = 2.6 for water, 1 in non associated solvents, 0.90 in this study
	Scheibel
		Where C = 8.2×10 11 , 8

*

.49×10 11 in this study Arnold A VOC A L found in this study summarized Table S.10

Table 5 . Physico-chemical properties at 293K of the four ILs selected for diffusion coefficients measurement.

 5

	Solvent	M L (g mol -1

Table 6 : Operating conditions simulated.

 6

	D col	Z	P
	(m)	(m)	(bar)

Table 8 : Mass-transfer coefficients, HTU and removal efficiencies in [AllylEt 2 S][NTf 2 ] (First case : k L and k G are deduced from the B-S theory and a° is deduced from the S-S-R theory; second case : k L , k G and a° are deduced from only the S-S-R theory).

 8

	VOC	B-S theory for k L and k G , S-S-R theory for a° 10 5 ×k L 10 2 ×k G 10 3 ×K L a° HTU	Eff	S-S-R theory for k L , k G and a° 10 5 ×k L 10 2 ×k G 10 3 ×K L a° HTU	Eff
		m s -1	m s -1	s -1	m	%	m s -1	m s -1	s -1	m	%
	Toluene 1.17	3.45	1.15	3.38	99.6	0.154	2.26	0.247	15.72 71.9
	DCM	1.89	4.25	3.31	1.17	42.8	0.249	2.64	0.467	8.33	14.5

Table 9 : Mass-transfer coefficients, HTU and removal efficiencies in [bmim][NTf 2 ] (First case : k L and k G are deduced from the B-S theory and a° is deduced from the S-S-R theory; second case : k L , k G and a° are deduced from only the S-S-R theory). VOC B-S theory for k L and k G , S-S-R theory for a° S-S-R theory for k L , k G and a° 10

 9 5 ×k L 10 2 ×k G 10 3 ×K L a° HTU Eff 10 5 ×k L 10 2 ×k G 10 3 ×K L a° HTU

	Eff

synthesized ionic liquids [START_REF] Biard | A simple and timesaving method for the masstransfer assessment of solvents used in physical absorption[END_REF].

New and more effective ionic liquids with large structure and with limited viscosities to enhance solute diffusion might be synthesized in the future, trying to optimize the affinity for a large panel of VOCs. Molecular simulations can provide valuable information to guide the design of such dedicated ionic liquids [START_REF] Delaunay | Interfacial structure of toluene at an ionic liquid/vapor interface: A molecular dynamics simulation investigation[END_REF].

Funding source

The authors want to thank the ANR for the founding support (ANR 12 BLAN 007 01).

Acknowledgments

The authors are very grateful to Sylvain Giraudet for his support using the IGA 003 and to Alicia Janeiro, Mickael Badin and Tiphaine Blanchard for their help. The authors are also very grateful to Gary Rochelle (University of Texas in Austin) for his kind answers to our questions.


A Guenego

S Mesrine

L Dartois

L Leenhardt

F Clavel-Chapelon

M Kvaskoff

Marie-Christine C Boutron-Ruault
email: marie-christine.boutron@gustaveroussy.fr

F Bonnet

Pascale Gerbouin-Rérolle

Lyan Hoang

Rafika Chait

Céline Kernaleguen

Maryvonne Niravong

Relation between hysterectomy, oophorectomy and the risk of incident differentiated thyroid cancer: the E3N cohort

Keywords: thyroid cancer, hysterectomy, fibroids, oophorectomy

Maxime Valdenaire, and Gwenaëlle Guillas

Introduction

Incidence of thyroid cancer has increased worldwide over the recent decades [START_REF] Schneider | New developments in the diagnosis and treatment of thyroid cancer[END_REF][START_REF] Colonna | Recent trends in incidence, geographical distribution, and survival of papillary thyroid cancer in France[END_REF]. Some established risk factors for thyroid cancer are known, such as ionizing radiation, benign thyroid disease, genetic predisposal and high body mass index (BMI) [START_REF] Schneider | New developments in the diagnosis and treatment of thyroid cancer[END_REF][START_REF] Clavel-Chapelon | Risk of differentiated thyroid cancer in relation to adult weight, height and body shape over life: the French E3N cohort[END_REF][START_REF] Trésallet | The incidence of papillary thyroid carcinoma and outcomes in operative patients according to their body mass indices[END_REF]. Based on epidemiological data, it has long been proposed that hormonal factors may determine or modulate the risk of thyroid cancer. Indeed, thyroid cancers are threefold more frequent in women than in men after puberty and incidence decreases after menopause [START_REF] Caini | Menstrual and reproductive history and use of exogenous sex hormones and risk of thyroid cancer among women: a meta-analysis of prospective studies[END_REF][START_REF] Derwahl | Estrogen and its role in thyroid cancer[END_REF]. A role of female hormones in the etiology of thyroid cancer has been suggested with a direct action of estrogens, via its receptors (ER), on proliferative and neoplastic disorders [START_REF] Derwahl | Estrogen and its role in thyroid cancer[END_REF]. However, the relationship between thyroid cancer risk and reproductive or hormonal factors is still debated, with contradictory and often inconclusive findings on the association between thyroid cancer and age at puberty, menopause, parity, breast-feeding or menopausal hormone therapy [START_REF] Caini | Menstrual and reproductive history and use of exogenous sex hormones and risk of thyroid cancer among women: a meta-analysis of prospective studies[END_REF][START_REF] Kabat | Menstrual and reproductive factors, exogenous hormone use, and risk of thyroid carcinoma in postmenopausal women[END_REF][START_REF] Zamora-Ros | Reproductive and menstrual factors and risk of differentiated thyroid carcinoma: the EPIC study[END_REF][START_REF] Wang | Increased risk of papillary thyroid cancer related to hormonal factors in women[END_REF].

Accepted Article

.

Hysterectomy is one of the most common surgical procedures in gynecology worldwide and is mainly performed in case of a benign disease such as fibroma and endometriosis, conditions which are associated with lifetime sex steroid hormone exposure [START_REF] Hammer | Global epidemiology of hysterectomy: possible impact on gynecological cancer rates[END_REF][START_REF] Braganza | Benign breast and gynecologic conditions, reproductive and hormonal factors, and risk of thyroid cancer[END_REF][START_REF] Yang | Early Life Adverse Environmental Exposures Increase the Risk of Uterine Fibroid Development: Role of Epigenetic Regulation[END_REF].

Several studies have attempted to determine hormonal and reproductive factors involved in the development of thyroid cancer in women, with conflicting results [START_REF] Caini | Menstrual and reproductive history and use of exogenous sex hormones and risk of thyroid cancer among women: a meta-analysis of prospective studies[END_REF][START_REF] Wang | Increased risk of papillary thyroid cancer related to hormonal factors in women[END_REF][START_REF] Cao | Reproductive Factors but Not Hormonal Factors Associated with Thyroid Cancer Risk: A Systematic Review and Meta-Analysis[END_REF]. A potential association between hysterectomy and thyroid cancer risk has already been described, but in studies with methodological heterogeneities and potential bias [START_REF] Kabat | Menstrual and reproductive factors, exogenous hormone use, and risk of thyroid carcinoma in postmenopausal women[END_REF][START_REF] Luoto | Increased risk of thyroid cancer among women with hysterectomies[END_REF][START_REF] Rossing | Reproductive Factors and Risk of Papillary Thyroid Cancer in Women[END_REF][START_REF] Truong | Role of goiter and of menstrual and reproductive factors in thyroid cancer: a population-based case-control study in New Caledonia (South Pacific), a very high incidence area[END_REF][START_REF] Altman | Long-term cancer risk after hysterectomy on benign indications: Population-based cohort study[END_REF]. Moreover, links between thyroid cancer risk and hysterectomy, oophorectomy, or benign gynecological disease histories have not been investigated simultaneously, despite common etiological factors and frequent morbid associations. Thus, we aimed to prospectively explore the link between differentiated thyroid cancer (micro or macro-carcinomas) and a history of hysterectomy, with or without oophorectomy, in a large cohort, according to age and time since gynecological surgery. In addition, we investigated the relation between a history of benign gynecological disease (uterine fibroids, endometriosis, ovarian cyst and uterine polyp and the risk of incident thyroid cancer.

Materials and Methods

The E3N cohort

The E3N cohort study (Etude Epidemiologique de Femmes de la Mutuelle Générale de l'Education Nationale) is a prospective cohort of 98,995 French women born between 1925 and 1950 and insured by a national health system primarily covering teachers [START_REF] Clavel-Chapelon | Cohort Profile: The French E3N Cohort Study[END_REF]. Participants have received 11 follow-up questionnaires (mailed every 2-3 years) and responded to each at a rate of ~80% [START_REF] Clavel-Chapelon | Cohort Profile: The French E3N Cohort Study[END_REF]. The women were enrolled in 1990 after they returned a baseline self-administered questionnaire on their lifestyle and medical history. All women signed an informed consent, in compliance with the rules of the French National Commission for Data Protection and Individual Freedom from which approval was obtained.

Thyroid disease assessment

Each questionnaire inquired about cancer occurrence, and requested information and permission to contact participants' physicians. Cases were confirmed by pathology reports [START_REF] Clavel-Chapelon | Cohort Profile: The French E3N Cohort Study[END_REF]. Here, we

Accepted Article

. considered only histologically confirmed first incident primary differentiated thyroid cancer cases (i.e. papillary (International Classification of Diseases for Oncology, ICD-O codes: 8050, 8052, 8130, 8260, 8263, 8340-8344, 8350, 8450) and follicular (8290, 8330-8335, 8480, 8490)), excluding 21 cases of anaplastic or medullary thyroid cancer. Micro-and macro-carcinomas were defined as tumors sized <10mm and ≥ 10mm, respectively.

Each questionnaire also inquired about diagnoses of dysthyroidism (hyperthyroidism or hypothyroidism), and of benign morphological thyroid conditions.

Assessment of hysterectomy and benign gynecological diseases

Hysterectomy and oophorectomy status (none, or uni-or bilateral), and age at surgery were recorded in each questionnaire. Benign gynecological diseases considered in this analysis were endometriosis, ovarian cysts, fibroids, and uterine polyps recorded in each questionnaire. Ovarian cysts reported by women diagnosed with endometriosis were not considered, to avoid potentially misdiagnosed ovarian endometrioid cyst cases. For all diseases, diagnostic procedures as laparoscopy, biopsy, hysterography, hysteroscopy, or ultrasonography were recorded in the 1992, 1993, and 1994 questionnaires and surgical treatments were available in each questionnaire except the baseline questionnaire. For each gynecological disease, we separately considered those confirmed by surgery or laparoscopy, confirmed by at least one treatment or diagnosis exam, and only self-reported gynecological diseases.

Population for analysis

Follow-up started at the date of return of the 1990 questionnaire. Participants contributed personyears of follow-up until the date of diagnosis of any cancer (except basal-cell carcinoma and in situ colorectal cancer), the date of the last completed questionnaire, or December 2011 (date of mailing of the 10th questionnaire), whichever occurred first. Women studied were censored at the date of a first thyroid cancer and we did not consider a hysterectomy or other benign gynecological diseases which occurred following a first thyroid cancer. Among the 98,995 women included in the study, we excluded those who reported a prevalent cancer at baseline other than a basal cell cancer or in situ colorectal cancer (n=4,844), and women with no follow-up data (n=2,073), with primary amenorrhea or unknown age at menarche (n=2209), with missing information on age at hysterectomy or oophorectomy (n= 418), or with unknown date of cancer diagnosis (n=111), ending up with 89,340 women for analysis.

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Statistical analyses

Cox proportional hazard models with age as time-scale were used to estimate Hazard Ratios (HR) and 95% confidence intervals (CI) of first differentiated thyroid cancer associated with history of hysterectomy or benign gynecological disease. Women diagnosed with non-differentiated thyroid cancer were censored at the date of diagnosis. Hysterectomy status or benign gynecological disease variables were analyzed as time-dependent variables. When the variables were not available at a given questionnaire, the preceding value was considered until the next known value. The proportional hazard hypothesis was verified for all time-independent variables of interest using log-log survivor plots. Covariates included in the models used are listed in Tables 2 and3. Information on timedependent variables was updated at each questionnaire Missing values for all adjustment variables were replaced by the modal value, as they were missing for less than 5% of women.

We performed stratified analyses to explore associations according to tumor size (micro-(<10 mm) or macro-(≥10 mm) carcinoma) using competing-risk models. Cases with missing values on tumor size were excluded from these analyses and analyses were performed in each strata by censoring the cases belonged to the other strata at date of diagnosis.

We used homogeneity tests to compare risk estimates across strata using the Wald chi-square statistic.

Smoking status and a history of dysthyroidism were evaluated as potential effect modifiers by adding an interaction term in the final model and testing statistical significance. All tests were two-sided and statistical significance (p-value) was set at the 0.05 level. All analyses were performed using Statistical Analysis Systems (SAS) software, version 9.3 (SAS Institute, Inc, Cary, North Carolina).

Results

Among 89,340 women considered in the present analysis, 412 cases of first primary differentiated thyroid cancer (381 papillary and 31 follicular) were diagnosed during 1,603,264 person-years of observation (median follow-up duration of 9.9 years for cases and 21.4 years for non-cases). Of the 412 cases of thyroid cancer, the information on the micro or macro carcinoma status was missing for 9. A total of 166 (41%) were considered as micro carcinoma (size <10 mm) and 237 were macrocarcinoma (size ≥10 mm).

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As shown in Table 1, the frequency of goiter/thyroid nodules was similar between women with an history of hysterectomy and those who did not have hysterectomy. The prevalence of excessive weight or obesity was higher among the women with an history of hysterectomy as compared to those without hysterectomy.

Hysterectomy/ Oophorectomy and risk of thyroid cancer Women with a history of hysterectomy had an increased risk of differentiated thyroid cancer (HR=2.05, 95%CI 1.65 -2.55; model 2), as compared to women without hysterectomy (Figure 1, Table 2). When considering types of hysterectomy/oophorectomy, the highest risk was observed for women with hysterectomy and uni-or bilateral oophorectomy (HR=2.21, 95%CI 1.67 -2.91). There was no association between oophorectomy alone and thyroid cancer risk. Risks were similar whatever the age at the hysterectomy or the time since hysterectomy. Associations were similar although slightly stronger after adjustment for reproductive factors (model 3) (Table 2). Results were similar for papillary and follicular cancers (HR=2.02, 95%CI 1.61-2.53 for papillary, HR=2.52, 95%CI 1.17-5.44 for follicular, P homogeneity =0.59, model 2). Both micro-and macro-carcinomas ((HR=1.81, 95%CI 1.28-2.57 and HR=2.16, 95%CI 1.62-2.88 respectively, P homogeneity =0.45, model 2) were associated with a history of hysterectomy.

The association between a history of hysterectomy and thyroid cancer risk was not modified by smoking status nor dysthyroidism history (P interaction = 0.09 and 0.23, respectively) and was observed in all corresponding strata.

Fibroids

Overall, a history of benign gynecological disease confirmed by surgery or laparoscopy was associated with increased thyroid cancer risk (HR 1.67, 95%CI 1.32 -2.11; model 2) (Table 3). The increase was driven by the association with uterine fibroids history (HR 1.91; 95 % CI 1.50 -2.44, model 2) (Table 3). This association was observed whatever the mode of diagnosis of fibroids and irrespective of a history of hysterectomy (Table 3). Women with a confirmed history of fibroids had an increased risk of both micro-(HR=1.54, 95%CI Neither self-reported nor confirmed history of endometriosis, uterine polyps or ovarian cysts were associated with thyroid cancer risk (Table 3). Results were similar for papillary and follicular thyroid cancers (data not shown).

Finally, we performed sensitivity analyses by excluding women who had an early diagnosis of thyroid cancer (first 2 years of follow up) and the results were unchanged: women with a history of hysterectomy had an increased risk of differentiated thyroid cancer (HR=2.01, 95%CI 1.60 -2.52; model 2), as compared to women without hysterectomy. Similarly, those who had a history of uterine fibroma were at higher risk of thyroid cancer as well (HR 1.84; 95 % CI 1.47 -2.30, model 2).

Discussion

In this large prospective study with more than 400 incident thyroid cancer cases occurring in women aged 40-65 at baseline, we found a positive relationship between the risk of differentiated thyroid cancer and a history of hysterectomy, but not with a history of oophorectomy. Results were similar whatever the age at hysterectomy or time since hysterectomy. We observed also an association between a history of fibroids and the risk of thyroid cancer, which appears to be independent of a history of hysterectomy.

Hysterectomy/oophorectomy status and risk of thyroid cancer

A recent meta-analysis reported an association between a history of hysterectomy and the risk of thyroid cancer with a summary relative risk (SRR) of 1.43 [START_REF] Caini | Menstrual and reproductive history and use of exogenous sex hormones and risk of thyroid cancer among women: a meta-analysis of prospective studies[END_REF]. However, the results were contrasting as only five out of 24 studies found that hysterectomy was associated with an increased risk of thyroid cancer. Other studies focusing specifically on the link between differentiated thyroid cancer risk and a history of hysterectomy were also conflicting [START_REF] Kabat | Menstrual and reproductive factors, exogenous hormone use, and risk of thyroid carcinoma in postmenopausal women[END_REF][START_REF] Braganza | Benign breast and gynecologic conditions, reproductive and hormonal factors, and risk of thyroid cancer[END_REF][START_REF] Luoto | Increased risk of thyroid cancer among women with hysterectomies[END_REF][START_REF] Rossing | Reproductive Factors and Risk of Papillary Thyroid Cancer in Women[END_REF][START_REF] Altman | Long-term cancer risk after hysterectomy on benign indications: Population-based cohort study[END_REF][START_REF] Luoto | Hysterectomy and subsequent risk of cancer[END_REF][START_REF] Wong | Reproductive history, occupational exposures, and thyroid cancer risk among women textile workers in Shanghai, China[END_REF]. Methodological flaws may partly explain these discrepancies, due to case-control design and retrospective self-reported surgery history. Besides, studies concluding that there was a positive relationship between a history of hysterectomy and thyroid cancer risk did not perform adjustment on history of benign thyroid disease

Accepted Article

. or family history of thyroid cancer, and thus could not discard the possibility of confounding [START_REF] Luoto | Increased risk of thyroid cancer among women with hysterectomies[END_REF][START_REF] Rossing | Reproductive Factors and Risk of Papillary Thyroid Cancer in Women[END_REF][START_REF] Altman | Long-term cancer risk after hysterectomy on benign indications: Population-based cohort study[END_REF][START_REF] Luoto | Hysterectomy and subsequent risk of cancer[END_REF].

In contrast to previous studies [START_REF] Luoto | Increased risk of thyroid cancer among women with hysterectomies[END_REF][START_REF] Rossing | Reproductive Factors and Risk of Papillary Thyroid Cancer in Women[END_REF][START_REF] Altman | Long-term cancer risk after hysterectomy on benign indications: Population-based cohort study[END_REF], we did not observe any change in the association between hysterectomy and the risk of thyroid cancer in relation to the time elapsed since hysterectomy or according to the age at hysterectomy. This finding is an argument against a potential detection bias associated to gynecological surgery. However, we cannot exclude such a detection bias. It could be speculated that thyroid cancer may be more likely to be found among women with hysterectomy or fibroids, because of medical attention received, as compared to those without the conditions. However, the slightly stronger relation observed between hysterectomy or fibroids and macro-cancers compared with micro-cancers is not in favor of a potential screening bias, which involved the detection of a majority of microcarcinoma.

Surgically-induced menopause, often defined in studies as hysterectomy and/or bilateral oophorectomy has previously been associated with an increased risk of thyroid cancer [START_REF] Zamora-Ros | Reproductive and menstrual factors and risk of differentiated thyroid carcinoma: the EPIC study[END_REF][START_REF] Truong | Role of goiter and of menstrual and reproductive factors in thyroid cancer: a population-based case-control study in New Caledonia (South Pacific), a very high incidence area[END_REF][START_REF] Negri | A pooled analysis of case-control studies of thyroid cancer. II. Menstrual and reproductive factors[END_REF].

When we considered simultaneously hysterectomy and oophorectomy status, we found that a history of oophorectomy was not related to the risk of thyroid cancer and did not substantially affect the association between hysterectomy and thyroid cancer. This is consistent with the WHI cohort for which Kabat et al [START_REF] Kabat | Menstrual and reproductive factors, exogenous hormone use, and risk of thyroid carcinoma in postmenopausal women[END_REF] did not find any association between thyroid cancer risk and bilateral oophorectomy. Some authors found either a higher [START_REF] Mack | Reproductive and hormonal risk factors for thyroid cancer in Los Angeles County females[END_REF], a lower [START_REF] Rossing | Reproductive Factors and Risk of Papillary Thyroid Cancer in Women[END_REF][START_REF] Altman | Long-term cancer risk after hysterectomy on benign indications: Population-based cohort study[END_REF] or a similar [START_REF] Braganza | Benign breast and gynecologic conditions, reproductive and hormonal factors, and risk of thyroid cancer[END_REF][START_REF] Luoto | Increased risk of thyroid cancer among women with hysterectomies[END_REF][START_REF] Truong | Role of goiter and of menstrual and reproductive factors in thyroid cancer: a population-based case-control study in New Caledonia (South Pacific), a very high incidence area[END_REF]) risk of thyroid cancer in women with hysterectomy and bilateral oophorectomy compared to women with hysterectomy alone or hysterectomy with partial oophorectomy.

Benign gynecological diseases history and risk of thyroid cancer

Our study revealed a positive association between a history of fibroids and the risk of differentiated thyroid cancer, which is consistent with the relationship between hysterectomy and thyroid cancer as uterine fibroids are the most common cause of hysterectomy [START_REF] Yang | Early Life Adverse Environmental Exposures Increase the Risk of Uterine Fibroid Development: Role of Epigenetic Regulation[END_REF]. The twofold increased risk of thyroid cancer linked to surgically treated fibroids was similar to results reported in two American studies [START_REF] Braganza | Benign breast and gynecologic conditions, reproductive and hormonal factors, and risk of thyroid cancer[END_REF][START_REF] Rossing | Reproductive Factors and Risk of Papillary Thyroid Cancer in Women[END_REF].

Studies on the relationship between endometriosis history and thyroid cancer risk are more conflicting, with HR/SIR varying between 0.85 and 3.09. Only two studies found an increased risk of thyroid cancer in women with an endometriosis evolving from more than 5 years [START_REF] Brinton | Cancer risk after a hospital discharge diagnosis of endometriosis[END_REF] and in parous Accepted Article . women [START_REF] Melin | The risk of cancer and the role of parity among women with endometriosis[END_REF]. It may reflect discrepancies in the definition of endometriosis cases, differences in the populations and the design of the studies: some used retrospective cohort of infertile women [START_REF] Brinton | Causes of infertility as predictors of subsequent cancer risk[END_REF], other used data extracted from inpatient and cancer registers [START_REF] Brinton | Cancer risk after a hospital discharge diagnosis of endometriosis[END_REF][START_REF] Melin | The risk of cancer and the role of parity among women with endometriosis[END_REF][START_REF] Melin | Endometriosis and the risk of cancer with special emphasis on ovarian cancer[END_REF] or self-reported endometriosis history [START_REF] Yang | Early Life Adverse Environmental Exposures Increase the Risk of Uterine Fibroid Development: Role of Epigenetic Regulation[END_REF].

As previous studies [START_REF] Braganza | Benign breast and gynecologic conditions, reproductive and hormonal factors, and risk of thyroid cancer[END_REF], we found no relationship between an ovarian cyst history and thyroid cancer risk, which is in line with the lack of link between oophorectomy and thyroid cancer in our study.

Our results seem not to be related to detection bias. Uterine fibroids are the most common pelvic tumors, occurring in nearly 70% of all reproductive-aged women [START_REF] Yang | Early Life Adverse Environmental Exposures Increase the Risk of Uterine Fibroid Development: Role of Epigenetic Regulation[END_REF]. Hyper-or hypothyroidism both enhance the likelihood of their diagnosis or treatment [START_REF] Sweet | Evaluation and management of abnormal uterine bleeding in premenopausal women[END_REF] by causing abnormal uterine bleeding, and have been linked with an increased risk of differentiated thyroid cancer [START_REF] Lee | The association between papillary thyroid carcinoma and histologically proven Hashimoto's thyroiditis: a meta-analysis[END_REF][START_REF] Pazaitou-Panayiotou | Thyroid cancer in patients with hyperthyroidism[END_REF]. However, the fact that we found a similar thyroid cancer risk whatever the time elapsed since surgery argues against this.

Moreover, the slightly stronger relation observed between hysterectomy or fibroids and macrocancers compared with micro-cancers is not in favor of a potential screening bias.

Potential mechanisms linking uterine fibroids and differentiated cancer thyroid

Uterine fibroids have been associated with thyroid nodules [START_REF] Spinos | Increased frequency of thyroid nodules and breast fibroadenomas in women with uterine fibroids[END_REF][START_REF] Kim | The relationship between thyroid nodules and uterine fibroids[END_REF] and hypothyroidism [START_REF] Ott | Overt hypothyroidism is associated with the presence of uterine leiomyoma: a retrospective analysis[END_REF] in transversal studies, suggesting shared mechanisms between fibroids and thyroid diseases. Both fibroids and thyroid cancers are thought to be sex steroid dependent.

If the link between hormonal factors and the risk of fibroids is well established [START_REF] Braganza | Benign breast and gynecologic conditions, reproductive and hormonal factors, and risk of thyroid cancer[END_REF], the relationship between sex hormones and thyroid cancer is much less characterized. Both estrogen receptors α (ER α) with a proliferative and anti-apoptotic function, and estrogen receptors β (ERβ) with a pro-apoptotic function, are expressed in normal and thyroid tumor cells. Thyroid cell proliferation and neoplastic development might depend on the imbalance between ER α and ERβ [START_REF] Derwahl | Estrogen and its role in thyroid cancer[END_REF][START_REF] Huang | Differential expression patterns and clinical significance of estrogen receptor-α and β in papillary thyroid carcinoma[END_REF]. Moreover, progesterone receptors have already been described in thyroid follicular cells, and progesterone has been shown to upregulate genes involved in thyroid function and growth on normal human thyroid cells in vitro [START_REF] Bertoni | Progesterone Upregulates Gene Expression in Normal Human Thyroid Follicular Cells[END_REF].

Besides, thyroid cancer cells and fibroids are both able to biosynthesize estradiol in situ through the action of aromatase [START_REF] Kawabata | Estrogen receptors (alpha and beta) and 17betahydroxysteroid dehydrogenase type 1 and 2 in thyroid disorders: possible in situ estrogen synthesis and actions[END_REF][START_REF] Borahay | Signaling Pathways in Leiomyoma: Understanding Pathobiology and Implications for Therapy[END_REF].

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. However, the link between hormonal factors and thyroid cancer remain inconclusive in several studies [START_REF] Caini | Menstrual and reproductive history and use of exogenous sex hormones and risk of thyroid cancer among women: a meta-analysis of prospective studies[END_REF][START_REF] Kabat | Menstrual and reproductive factors, exogenous hormone use, and risk of thyroid carcinoma in postmenopausal women[END_REF][START_REF] Zamora-Ros | Reproductive and menstrual factors and risk of differentiated thyroid carcinoma: the EPIC study[END_REF][START_REF] Wang | Increased risk of papillary thyroid cancer related to hormonal factors in women[END_REF] suggesting that not only direct estrogen action but other pathways may be shared between fibroids and thyroid cancer, such as growth factors pathways and TSH/ thyroid hormones induced pathways. Growth factors and non-genomic estradiol pathways converge towards the aberrant activation of Ras/Raf/MEK/ERK and PI3K/Akt/mTOR signaling in both thyroid and fibroids cells. In addition, due to common nucleotide sequence in ER and thyroid hormone receptor, these receptors can interact and regulate several transcriptional responses to environmental stimuli [START_REF] Zane | Estrogens and stem cells in thyroid cancer[END_REF]. Moreover, thyrotropin-releasing hormone (TRH), thyroid-stimulating hormone (TSH), and thyroid hormone receptors were shown to be present in monkey uterus [START_REF] Hulchiy | Receptors for thyrotropin-releasing hormone, thyroid-stimulating hormone, and thyroid hormones in the macaque uterus: effects of long-term sex hormone treatment[END_REF]. Another study described a smooth muscle cells proliferation after stimulation by TSH [START_REF] Fröhlich | Mechanisms in Endocrinology: Impact of isolated TSH levels in and out of normal range on different tissues[END_REF].

Somatic genetic mutations play a part in the molecular pathogenesis of both fibroids (MED12 mutations) [START_REF] Yang | Early Life Adverse Environmental Exposures Increase the Risk of Uterine Fibroid Development: Role of Epigenetic Regulation[END_REF] and differentiated thyroid cancer (eg BRAF mutations) [START_REF] Schneider | New developments in the diagnosis and treatment of thyroid cancer[END_REF]. Thus a chronic reduction in DNA repair capacity might explain partly a common susceptibility to differentiated thyroid cancer and fibroids. The increased risk of both thyroid cancer and fibroids in atomic bomb survivors illustrates this hypothesis [START_REF] Douple | Long-term radiation-related health effects in a unique human population: lessons learned from the atomic bomb survivors of Hiroshima and Nagasaki[END_REF]. Increased insulin resistance or related hyperinsulinemia might be a common underlying factor shared by women with uterine fibroids which may predispose to the development of thyroid cancer as recently suggested (41).

Strengths and limits

Strengths of our study include its prospective design, large sample size, histological confirmation of all thyroid cancer cases, and availability of data for most differentiated risk factors including a history of benign thyroid conditions. Exposure data were collected before diagnosis of thyroid cancer, avoiding potential recall biases. To our knowledge, it is the first study that investigated an association between hysterectomy, uterine fibroids and micro-and macro-thyroid cancer risk. This cohort is not representative of the French population and our results cannot be extrapolated to the entire French population. As in all observational studies, residual confounding may subsist.

Misclassification of exposure status is a potential limitation because of the self-reported assessment of surgery, benign gynecological and thyroid diseases. Moreover, when we restricted the analysis to the treated cases, the associations remain consistent. Women included in our study, although

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. younger than in the WHI and PLCO studies, were mostly postmenopausal, and our results may not be generalizable to young premenopausal women.

Conclusion

Our findings showed that hysterectomy or a history of fibroids were associated with a twofold increased risk of differentiated thyroid cancer (micro-and macro-carcinomas) in mostly postmenopausal women. This relation might be explained by common signaling pathways regulated by estrogen, progesterone, or TSH/thyroid hormones. Further studies are needed to delineate the underlying molecular mechanisms or pathways.

41. Malaguarnera R, Vella V, Nicolosi ML, Belfiore A. Insulin Resistance: Any Role in the Changing Epidemiology of Thyroid Cancer? Front Endocrinol (Lausanne). 2017;8:314.

  1.03-2.30, model 2) and macro-carcinomas (HR=2.16, 95%CI 1.57-2.97, model 2). If we consider simultaneously history of hysterectomy and of fibroids in the same multivariate statistical model (model 2), each variable remains statistically associated with risk of thyroid cancer [hysterectomy (yes/no): HR=1.70, 95% CI :1.27 -2.28; history of fibroids (yes/no): HR=1.33, 95% CI :1.01 -1.75].

	Accepted Article
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the

Table 1 : Patients characteristics according to baseline hysterectomy status. E3N cohort, 1990-2011 (n=89,340)

 1

	No hysterectomy (n = 80,197)	Hysterectomy (n = 9143)
	n	(%)	n	(%)

Body mass index, (kg/m²)

	Ever	46,553	(58.0)	3143	(34.4)
	Infertility treatment
	<18.5 [18.5-22.5[ [22.5-25[ [25-30[ ≥30 Age at menarche (years) <13 ≥13 Use of oral contraceptives Never Never Ever Parity and age at first full-term pregnancy Nulliparous One child at age <30 One child at age ≥30 2 or more children, the first at age <30 2 or more children, the first at age ≥30 Menopausal status and use of MHT at baseline Premenopausal Postmenopausal with no recent use of MHT Postmenopausal with recent use of MHT Accepted Article Postmenopausal with unknown use of MHT	3479 43,894 19,659 10,932 2233 36,754 43,443 33,644 74,269 5928 8987 8956 3848 53,274 5132 51,692 16,273 7446 4786	(4.4) (54.7) (24.5) (13.6) (2.8) (45.8) (54.2) (42.0) (92.6) (7.4) (11.2) (11.2) (4.8) (66.4) (6.4) (64.5) (20.3) (9.3) (6.0)	250 3980 2607 1870 436 4463 4680 6000 8499 644 1278 1201 280 6072 312 2245 3749 1875 1274	(2.7) (43.5) (28.5) (20.5) (4.8) (48.8) (51.2) (65.6) (93.0) (7.0) (14.0) (13.1) (3.1) (66.4) (3.4) (24.6) (41.0) (20.5) (13.9)
	.

Menopausal status at the end of the follow-up

	Premenopausal	4828	(6.0)	148	(1.6)
	Postmenopausal	75,369	(94.0)	8995	(98.4)

Age at menopausal at the end of follow-up

	Mean ± standard deviation	51.0	± 3.5	47.3	± 5.7

The authors declare no potential conflicts of interest Funding/support: This work was supported by the Mutuelle Générale de l'Education Nationale (MGEN); the European Community; the French League against Cancer (LNCC); Gustave Roussy; and the French National Institutes for Health and Medical Research (Inserm) The present study received grant support from the French National Cancer Institute (InCA) (#2009-139).

Role of the sponsors: Funding sources had no involvement in the design and carrying out of the study, collection, management, analysis and interpretation of data, or preparation, review and approval of the manuscript.

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.

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. M3: M2 further adjusted for age at menarche (<13 years/≥13 years), use of oral contraceptives (ever/never, time-dependent), infertility treatment (ever/never, last assessed in 1992), parity and age at first full-term pregnancy (nulliparous/one child at age <30/one child at age ≥30/two children or more, the first at age <30/two children or more, the first at age ≥30), age at menopause and use of MHT (premenopausal/postmenopausal with no recent use of MHT/postmenopausal with recent use of MHT/postmenopausal with use of MHT but unknown recency, time-dependent).