Marie Décultot

Alain Ledoux
email: alain.ledoux@insa-rouen.fr

Marie-Christine Fournier-Salaün

Lionel Estel

Kinetic modelling of the synthesis of diethyl carbonate and propylene carbonate from ethanol and 1,2-propanediol associated with CO 2

Keywords:

Organic carbonates have attracted considerable attention because of their numerous applications. The direct association of CO 2 and alcohol to synthesise these carbonates is one of the most promising routes, when considering the economic and the environmental aspects. A significant number of researchers have worked on the catalysis and the dehydration of these reactions, but very few have dealt with the study of the thermodynamic equilibrium and the kinetics of these reactions. The objective of this work is to study the synthesis of diethyl carbonate (DEC) and propylene carbonate (PC). A parametric study was conducted by varying the temperature, the pressure and the initial concentration. Equilibrium constants were determined experimentally and compared to available published data. Kinetic models are developed based on four mechanisms, two of which are the mechanisms of Langmuir-Hinshelwood and Eley-Rideal. Mean deviations between the experimental data and the modelling were below 10 % for all the mechanisms. The best fit was obtained for the mechanism of Langmuir-Hinshelwood for the synthesis of DEC and PC. Activation energies of 100 kJ/mol and 77 kJ/mol were determined for the synthesis of DEC and PC, respectively.

Introduction

Organic carbonates like dimethyl carbonate (DMC), diethyl carbonate (DEC) or propylene carbonate (PC) have attracted considerable attention over recent decades because of their specific properties [START_REF] Kindermann | Synthesis of Carbonates from Alcohols and CO 2[END_REF][START_REF] Sakakura | The synthesis of organic carbonates from carbon dioxide[END_REF]. They are considered to be building blocks in the chemical industry to produce polycarbonates or more complex carbonates [START_REF] Ochoa-Gómez | Synthesis of glycerol carbonate from glycerol and dimethyl carbonate by transesterification: Catalyst screening and reaction optimization[END_REF]. They can also replace the highly toxic and hazardous phosgene in some reactions, like the synthesis of polyurethane [START_REF] Fukuoka | A novel non-phosgene polycarbonate production process using by-product CO 2 as starting material[END_REF]. Because of their low toxicity, organic carbonates can be used in replacement of some toxic or harmful solvents, like dichloromethane or toluene [START_REF] Miao | Dimethyl Carbonate: An Eco-Friendly Solvent in Ruthenium-Catalyzed Olefin Metathesis Transformations[END_REF]. DMC and DEC are often used as co-solvents in lithium batteries [START_REF] Takeuchi | Electrochemical lithium ion intercalation into graphite electrode in propylene carbonate-based electrolytes with dimethyl carbonate and calcium salt[END_REF] and also as a gasoline additive [START_REF] Pandian | Investigations on emission characteristics of the pongamia biodiesel-diesel blend fuelled twin cylinder compression ignition direct injection engine using exhaust gas recirculation methodology and dimethyl carbonate as additive[END_REF][START_REF] Szori | Glycerol carbonate as a fuel additive for a sustainable future[END_REF].

Conventionally, carbonates are produced by using certain highly toxic and harmful chemicals, like phosgene. To develop the market, a greener way of synthesis has to be found. New alternatives have been proposed in recent years [START_REF] Huang | Recent advances in dialkyl carbonates synthesis and applications[END_REF]. The most advanced alternative is the oxidative carbonylation of methanol or of methyl nitrile with CO. This synthesis is the most favourable in respect of thermodynamics, but it does use some toxic and corrosive chemicals. Today, new routes are being developed using CO 2 . Indeed, reactions of CO 2 utilisation have been in development over the past few decades because CO 2 is a nontoxic and abundant molecule. The idea is to transform the most emitted greenhouse gas into valuable products to replace classical synthesis, which uses oil-derivated products. In the case of organic carbonates, three routes are emerging. The first is the alcoholysis of urea generating carbonates during which NH 3 is evolved which can be converted back to urea by reacting with CO 2 . The second is the transesterification of cyclic carbonates, which is performed in two steps: CO 2 reacts with epoxide to produce cyclic carbonate, which will then react with alcohol to produce linear carbonate. The last route is the direct association of CO 2 and alcohol to produce carbonate. A recent study highlights that this direct synthesis is one of the most promising routes, when considering the economic and the environmental aspects [START_REF] Monteiro | Sustainability metrics for eco-technologies assessment, part I: preliminary screening[END_REF]. Indeed, the only co-product of this synthesis is water, and the alcohol which can be produced from biomass, like it is for methanol [START_REF] Galindo Cifre | Renewable hydrogen utilisation for the production of methanol[END_REF], ethanol [START_REF] Sirajunnisa | Algae -A quintessential and positive resource of bioethanol production: A comprehensive review[END_REF] or 1,2-propanediol [START_REF] Marinas | Sustainability metrics for a fossil-and renewable-based route for 1,2-propanediol production: A comparison[END_REF].

The growing interest in organic carbonates synthesis and CO 2 utilisation is leading researchers to work on this reaction. In the literature, many catalysts have been proposed; however, the yields obtained are still very low due to the unfavourable thermodynamics of the reaction (Honda et al., 2014a;[START_REF] Kindermann | Synthesis of Carbonates from Alcohols and CO 2[END_REF][START_REF] Tamboli | Catalytic developments in the direct dimethyl carbonate synthesis from carbon dioxide and methanol[END_REF]. Indeed, the reaction reaches a thermodynamic equilibrium. Removing water from the reaction mixture can shift this equilibrium and improve yields in carbonate. This dehydration can be made by using a dehydrating agent like ketals [START_REF] Tomishige | Catalytic and direct synthesis of dimethyl carbonate starting from carbon dioxide using CeO 2 -ZrO 2 solid solution heterogeneous catalyst: effect of H2O removal from the reaction system[END_REF], acetonitrile [START_REF] Honda | Catalytic synthesis of dialkyl carbonate from low pressure CO 2 and alcohols combined with acetonitrile hydration catalyzed by CeO 2[END_REF][START_REF] Honda | Low pressure CO 2 to dimethyl carbonate by the reaction with methanol promoted by acetonitrile hydration[END_REF], benzonitrile (Honda et al., 2014a) or 2-cyanopyridine [START_REF] Tomishige | CO 2 Conversion with Alcohols and Amines into Carbonates, Ureas, and Carbamates over CeO 2 Catalyst in the Presence and Absence of 2-Cyanopyridine -Tomishige --The Chemical Record -Wiley Online Library[END_REF]. This method improves the yield, but raises certain issues, like the separation of products and co-products at the end of the reaction. Some physical dehydration has been tested, such as the use of a molecular sieve [START_REF] Choi | Selective and high yield synthesis of dimethyl carbonate directly from carbon dioxide and methanol[END_REF] or a hydrophilic membrane (Décultot et al., 2019a;[START_REF] Dibenedetto | Synthesis, Characterization, and Use of NbV/CeIV-Mixed Oxides in the Direct Carboxylation of Ethanol by using Pervaporation Membranes for Water Removal[END_REF][START_REF] Li | Study on application of membrane reactor in direct synthesis DMC from CO 2 and CH 3 OH over Cu-KF/MgSiO catalyst[END_REF]. These methods are efficient to improve yields, but more studies are required in order to identify the best conditions of use [START_REF] Aresta | Energy issues in the utilization of CO 2 in the synthesis of chemicals: The case of the direct carboxylation of alcohols to dialkyl-carbonates[END_REF].

A significant number of researchers have worked on the catalysis and the dehydration of these reactions, but very few works deal with the study of the thermodynamic equilibrium and the kinetics of these reactions. However, these data are essential to understand the limitation of these reactions in order to find efficient solutions to improve the yields. Only three articles have studied the kinetics of the reaction of the synthesis of dimethyl carbonate [START_REF] Fu | TiO 2 -Doped CeO 2 Nanorod Catalyst for Direct Conversion of CO 2 and CH 3 OH to Dimethyl Carbonate: Catalytic Performance and Kinetic Study[END_REF][START_REF] Marin | Kinetic and mechanistic investigations of the direct synthesis of dimethyl carbonate from carbon dioxide over ceria nanorod catalysts[END_REF][START_REF] Santos | Kinetic study for the direct synthesis of dimethyl carbonate from methanol and CO 2 over CeO 2 at high pressure conditions[END_REF]. In each case, the initial kinetics are studied to estimate the activation energy. Two articles studied the kinetics based on the mechanisms of Langmuir-Hinshelwood and Eley-Rideal [START_REF] Marin | Kinetic and mechanistic investigations of the direct synthesis of dimethyl carbonate from carbon dioxide over ceria nanorod catalysts[END_REF][START_REF] Santos | Kinetic study for the direct synthesis of dimethyl carbonate from methanol and CO 2 over CeO 2 at high pressure conditions[END_REF]. However, the rate laws developed are different in the two articles.

The aim of this study is to develop a kinetic model for the synthesis of DEC and PC, for which no data has yet been found in the literature (Eq 1 and 2). A parametric study was performed using the catalyst CeO 2 , which gives good yields and very high selectivity [START_REF] Yoshida | Direct synthesis of organic carbonates from the reaction of CO 2 with methanol and ethanol over CeO 2 catalysts[END_REF]. Thermodynamic constants were evaluated experimentally for different experimental conditions and compared with thermodynamic data found in the literature. Several kinetic models were developed based on different mechanisms, and rate constants were identified with the experimental data. The influence of several parameters such as temperature, pressure and initial concentrations of water and carbonates were studied.

Eq 1 CO 2 2 H 2 O + + DEC O O O Ethanol l OH Eq 2

2.

Materials and methods

Materials

Cerium (IV) oxide with a purity of 99.5 % was purchased from Alfa Aesar. This catalyst was calcined at 600 °C for 4 h in the air. Absolute ethanol (>99.7 %) was purchased from VWR, DEC (>99 %) and 1,2propanediol (>99,5 %) were purchased from Alfa Aesar and PC (>99 %) from Sigma Aldrich. All products were used as received.

Reactor unit

The reactor unit used to conduct the parametric study has been described in a previous work (Décultot et al., 2019a). A Parr autoclave with a capacity of 100 mL was used. It is equipped with a blade agitator, a valve to take samples during the reaction and two valves to add or remove CO 2 . The temperature is controlled, and the pressure is read on a pressure gauge. For a typical experiment, 50 mL of ethanol are filled in the reactor with 2 g of CeO 2 . Then, the reactor is purged three times with CO 2 . Subsequently, the CO 2 is filled at the desired pressure by waiting for its solubilisation in ethanol for 45 min. The temperature is then increased up to the desired temperature. 1 mL of the sample is taken at selected times during the reaction. At the end of the reaction, the reactor is cooled down, and the pressure is decreased. For the determination of the concentrations of alcohol and carbonate, samples are diluted in methanol, with hexanol as an internal standard, and they are analysed by gas chromatography with a flame ionisation detector (FID) with an accuracy of 4 % (cf appendix for typical chromatogram). The initial amount of water was determined by a Karl-Fischer titration with a coulometric method, with an accuracy of 10 %. The protocol is similar for the reaction with 1,2-propanediol, but the solution is diluted in ethanol for the analysis. Table 1 presents the reaction operating conditions used for the experiments.

Experiments can be classified into four groups. The first three correspond to the synthesis of DEC. The first one concerns reactions performed at different temperatures and similar pressures. For the second group, pressure was varied, but the temperature was the same. In the third group, different initial concentrations of water and diethyl

3.

Results and discussion

Thermodynamic equilibrium

For the kinetic modelling, reaction equilibrium data are necessary. In the case of CO 2 , there is an equilibrium between the gas and the CO 2 dissolved in the solvent. The activity of CO 2 can be expressed using a pressure or a concentration. For the concentration, the activity can be replaced by a concentration ratio using a reference concentration. With the same reference concentration for all compounds except CO 2 , equation can be simplified by elimination of the reference concentration. The equilibrium constant ( ) is calculated based on the activity ( ) and the stoichiometric coefficient ) of each component at the equilibrium (Eq 3). The activities of alcohol, carbonate and water can be expressed with concentrations. These two parameters are related by the Henry's law (Décultot et al., 2019b). In our case, pressure was chosen to simplify the expression. This approximation is justified by the fact that the conversion of alcohol is very low, assuming that CO 2 consumption is negligible, so the pressure is quite constant during all the experiments. Equilibrium constants are calculated with Eq 4 and Eq 5 for the synthesis of DEC and PC, respectively. and represent the standard pressure and concentration equal to 1 bar and 1 mol/L, respectively.

Eq 3 Eq 4

Eq 5

To ascertain the concentration of each component at equilibrium, reactions were performed over a long period of time (>24 h). The equilibrium is assumed to be reached when the concentration of DEC measured becomes constant. Concentrations of the other components are calculated from DEC and PC concentrations at the equilibrium:

Eq 6 Eq 7 2 for the four groups of reactions. Equilibrium constants are calculated only when the equilibrium is reached. For some reactions, the time was not long enough for the DEC concentration to become constant. For group 3, it can be seen that similar equilibrium constants are obtained with different initial concentrations of water and DEC. This result confirms that the thermodynamic equilibrium is reached for each reaction. Concerning the effect of temperature, the equilibrium constant seems to

𝐾 𝑒𝑞 = 𝑎 𝑖 𝜈 𝑖 𝐾 𝑒𝑞 = [𝐷𝐸𝐶] 𝑒𝑞 [𝐻 2 𝑂] 𝑒𝑞 𝑃 [𝐸𝑡𝑂𝐻] 𝑒𝑞 2 𝑃 𝐶𝑂2 𝐾 𝑒𝑞 = [𝑃𝐶] 𝑒𝑞 [𝐻 2 𝑂] 𝑒𝑞 𝑃 𝐶 [1,2𝑃𝑃𝐷] 𝑒𝑞 𝑃 𝐶𝑂2 [𝐻 2 𝑂] 𝑒𝑞 = [𝐻 2 𝑂] + [𝐷𝐸𝐶] 𝑒𝑞 [𝐸𝑡𝑂𝐻] 𝑒𝑞 = [𝐸𝑡𝑂𝐻] -2[𝐷𝐸𝐶] 𝑒𝑞
[1,2𝑃𝑃𝐷] 𝑒𝑞 = [1,2𝑃𝑃𝐷] -[𝑃𝐶] 𝑒𝑞
decrease when the temperature increases for the synthesis of DEC (group 1), and for the synthesis of PC (group 4) the contrary is true. It can also be seen that the equilibrium constant of synthesis of PC is 100 times higher than the equilibrium constant for the synthesis of DEC.

No experimental data are available in the literature about the determination of this equilibrium constant for the synthesis of DEC and PC. However, it is possible to compare it with theoretical values by using the Gibbs free energy at the temperature T ( ) (Eq 9), calculated with the standard enthalpy of reaction and the standard entropy of reaction (Error! Reference source not found.Eq 12). These data are calculated using the standard enthalpy of formation , the standard entropy and the heat capacity of each component .

By combining Eq 11, Eq 12 and Eq 13, it is possible to calculate directly the equilibrium constant (Eq 14).

Eq 9

Eq 10

Eq 11

Eq 12

Eq 13

Eq 14

Table 3 shows the values of the standard enthalpy of formation and entropy of each component available in the literature, for the synthesis of DEC and the synthesis of PC [START_REF] Vasil'ev | Heat capacity and thermodynamic functions of propylene carbonate[END_REF][START_REF] Gardner | The standard enthalpies of formation of some aliphatic diols[END_REF][START_REF] Gardner | The standard enthalpies of formation of some aliphatic diols[END_REF][START_REF] Moureu | Heats of formation of ethylene oxide, of ethanediol and some of their homologs[END_REF][START_REF] Zaripov | Experimental study of the isobaric heat capacity of liquid organic compounds with molecular weights of up to 4000 a.e.m. Teplomassoobmen Teplofiz[END_REF][START_REF] Choi | Heats of combustion, heats of formation, and vapor pressures of some organic carbonates. Estimation of carbonate group contribution to heat of formation[END_REF][START_REF] Vasil'eva | Enthalpies of combustion of alkylene carbonates[END_REF][START_REF] Leino | Enhanced yields of diethyl carbonate via one-pot synthesis from ethanol, carbon dioxide and butylene oxide over cerium (IV) oxide[END_REF]Shukla and Srivastava, 2018). For the synthesis of DEC, values given by Leino and colleagues and Shukla and colleagues are different. The data of Leino and colleagues are for gas components, and the data of Shukla and colleagues are for the liquid components, except for CO 2 which is considered as a gas in both cases. Liquid heat capacity was used for DEC, water and ethanol, and the gaseous heat capacity was used for CO 2 . These data were found in the National Institute of Standards and Technology database (NIST). The influence of the value of heat capacity on the calculation of the equilibrium constant is negligible compared to the enthalpy and entropy. To simplify the calculations, these heat capacities are assumed to be constant in the range of temperature studied (in line with the procedure used by Leino et al. in their calculations).

Table 3. Standard enthalpy of formation, entropy and heat capacity of each component for the synthesis of DEC and PC

For the synthesis of PC, very limited data are available for the enthalpy, entropy and heat capacity of PC and 1,2propanediol. The uncertainties surrounding these data are high, and this has an important impact on the calculation of the Gibbs free energy. In a more recent publication, Verevkin and colleagues confirm the formation enthalpy of PC [START_REF] Verevkin | Cyclic alkylene carbonates. Experiment and first principle calculations for prediction of thermochemical properties[END_REF]. The value found was -614.1 ± 0.8 kJ/mol, which is near to that of Vasil'eva and colleagues [START_REF] Vasil'eva | Enthalpies of combustion of alkylene carbonates[END_REF]. This value was chosen in this study for the calculation of equilibrium constants. For the 1,2-propanediol, two cases were studied: a) case 1, with the enthalpy of -486 kJ/mol [START_REF] Gardner | The standard enthalpies of formation of some aliphatic diols[END_REF]; and b) case 2, with a value of -500.3 kJ/mol [START_REF] Moureu | Heats of formation of ethylene oxide, of ethanediol and some of their homologs[END_REF].

Only one value of entropy and one value of heat capacity were found for both PC and 1,2-propanediol. Recently, Yasir and colleagues tried to calculate the reaction enthalpy of the synthesis of PC, but the data used were different from those presented here, and the sources do not permit us to find the values [START_REF] Yasir | Synthesis of Propylene Carbonate from Propane-1,2-diol and Urea Using Hydrotalcite-Derived Catalysts[END_REF]. We chose not to use these values.

Equilibrium constants for the synthesis of DEC were calculated using the data of Leino and colleagues and with the data of Shukla and colleagues, using liquid heat capacities with Eq 13. close to the data obtained by Shukla and Leino. For each case, the equilibrium constant decreases with increasing temperature. Table S2 compares the values of equilibrium constants obtained experimentally and those calculated with the data found in the previous studies for the synthesis of PC. The enthalpy of formation of 1,2-

propanediol has an important impact on the equilibrium constant. Between case 1 and 2, the values differ by two orders of magnitude for 393 K. The experimental results are closer to case 2. However, the equilibrium constant decreases when the temperature increases. Experimentally, it is the opposite. The uncertainties of the experimental data and the high uncertainties of the data can explain this difference of tendency.

Eq 15 is obtained by combining Eq 12 and Eq 14. By considering that the enthalpy and entropy of the reaction are constant within the temperature range studied, these two parameters can be estimated by plotting ln against the inverse of temperature. The results are presented in Figure 1 : Estimation of the enthalpy and the entropy of the reaction by plotting ln K eq against 1/T for the experimental results and the thermodynamic data of Leino and colleagues and Shukla and colleagues and Table 4 for the synthesis of DEC.

Eq 15

Figure 1 : Estimation of the enthalpy and the entropy of the reaction by plotting ln K eq against 1/T for the experimental results and the thermodynamic data of Leino and colleagues and Shukla and colleagues, for the synthesis of DEC. estimate the theoretical enthalpy and entropy does not take into account the pressure. For the experimental data, the pressure was not exactly the same for each experiment. This factor may influence the enthalpy and entropy of the reaction. To be coherent with our experiments, equilibrium constants for other reactions at different temperatures (R2, R3, R6 and R7) are estimated with Eq 14 by using = -9.4 kJ/mol and = -153 J/mol/K. These values were also used to estimate the equilibrium constant of the reaction with a variation of initial concentrations (R12-R16). The same equilibrium constant of 1.79•10 -7 was used for all calculations because the temperature and the pressure were the same.

To estimate the equilibrium constant of R17 and R18 in the case of the synthesis of PC, Eq 14 was used

(Figure 2). The tendency of the experimental data for the variation of the equilibrium constant with the temperature is not in accordance with the physical behaviour. Anyway, considering that only 4 values have been calculated in a short temperature range (20 K) with an important uncertainty, these points could be in agreement of a positive slope leading to a slightly negative enthalpy as proposed in literature. The enthalpy of case 2 was -3.2 kJ/mol and for the entropy was -101 J/mol/K. The experimental enthalpy and entropy of reaction were used to calculate the equilibrium constant of R17 and R18. rate laws for the kinetic modelling of the synthesis of DMC from methanol and CO 2 [START_REF] Marin | Kinetic and mechanistic investigations of the direct synthesis of dimethyl carbonate from carbon dioxide over ceria nanorod catalysts[END_REF][START_REF] Santos | Kinetic study for the direct synthesis of dimethyl carbonate from methanol and CO 2 over CeO 2 at high pressure conditions[END_REF]. These mechanisms are represented in Error! Reference source not found. (mechanism A and B).

In the case of the Langmuir-Hinshelwood mechanism, both CO 2 and ethanol are adsorbed on the catalyst. CO 2 and one molecule of ethanol adsorb on basic sites, and the second molecule of ethanol adsorbs on the acid sites [START_REF] Kumar | Dimethyl carbonate synthesis from carbon dioxide using ceria-zirconia catalysts prepared using a templating method: characterization, parametric optimization and chemical equilibrium modeling[END_REF][START_REF] Wang | Morphology control of ceria nanocrystals for catalytic conversion of CO 2 with methanol[END_REF]. They react together in step 3, and products desorb in steps 4 and 5. In the case of the Eley-Rideal mechanism, only ethanol is adsorbed on the catalyst, and an intermediate is formed in step 3. This intermediate is an ethylcarbonate (C 2 H 5 OCOO), which is described in some mechanisms used in other published works [START_REF] Eta | Kinetics of dimethyl carbonate synthesis from methanol and carbon dioxide over ZrO2-MgO catalyst in the presence of butylene oxide as additive[END_REF]Tomishige et al., 2000b). Some researchers experimentally studied the reaction to propose mechanisms that are more specific [START_REF] Aresta | Influence of Al 2 O 3 on the performance of CeO2 used as catalyst in the direct carboxylation of methanol to dimethylcarbonate and the elucidation of the reaction mechanism[END_REF][START_REF] Chen | Dimethyl carbonate synthesis from carbon dioxide and methanol over CeO 2 versus over ZrO 2 : comparison of mechanisms[END_REF]. The mechanisms depend on the catalyst used and on the experimental conditions. Mechanism C is based on the Langmuir-Hinshelwood mechanism, but the second molecule of ethanol does not adsorb on the catalyst. This hypothesis is based on the fact that it can be difficult to have a termolecular mechanism, and it is more likely that the second ethanol will not be adsorbed on the catalyst [START_REF] Aresta | Influence of Al 2 O 3 on the performance of CeO2 used as catalyst in the direct carboxylation of methanol to dimethylcarbonate and the elucidation of the reaction mechanism[END_REF]. Mechanism D corresponds to the mechanism developed by Chen and colleagues in the case of the synthesis of DMC with the catalyst CeO 2 . It is based on the Eley-Rideal mechanism, its first two steps are similar to those of the Langmuir-Hinshelwood mechanism, but the CO 2 and the first molecule of ethanol will be adsorbed on the catalyst. The intermediate detected by Raman spectrometry is also different from that of Eley-Rideal, in that it is a carbomethoxy (EtOCO=C 2 H 5 OCO) [START_REF] Chen | Dimethyl carbonate synthesis from carbon dioxide and methanol over CeO 2 versus over ZrO 2 : comparison of mechanisms[END_REF]. (Honda et al., 2014b).

This mechanism corresponds to the Eley-Rideal mechanism. In this study, two mechanisms are used: Eley-Rideal and Langmuir-Hinshelwood.

The controlling step is assumed to be the step of reacting between CO 2 and alcohol for each mechanism.

The other elementary steps are considered to be at the equilibrium and are defined with their equilibrium constant, named the letter subscript corresponds to the mechanism and the number subscript corresponds to the elementary step. For the case of the synthesis of PC, the letters PC are added in superscript. To define these equilibrium constants, the parameter  * was used, which represents the fraction of free active sites. represents the fraction of active sites occupied by the component i (Eq 16). The equilibrium constants are described for the case of the Langmuir-Hinshelwood mechanism for the synthesis of DEC in Eq 17.

Eq 16

Eq 17

The reaction rate is equal to the rate of step 3 in the case of mechanism A (Eq 18). The fraction of active sites for each component is replaced by using the equilibrium constant of each step. The rate law described in Eq 19 is obtained.

Eq 18

Eq 19

This equation corresponds to the equation usually obtained for the Langmuir-Hinshelwood mechanism [START_REF] Santos | Kinetic study for the direct synthesis of dimethyl carbonate from methanol and CO 2 over CeO 2 at high pressure conditions[END_REF]. The equilibrium constants used are those determined experimentally in section 3.1. The rate laws for other mechanisms and for the PC synthesis are developed by the same method and are detailed in Error! Reference source not found. to Eq 24.

Eq 20

Eq 21

1 = * + 𝐶𝑂2 + 𝐸𝑡𝑂𝐻 + 𝐷𝐸𝐶 + * 𝐻2𝑂 𝐾 𝐴 = 𝐶𝑂2 𝑃 𝑃 𝐶𝑂2 * 𝐾 𝐴2 = 𝐸𝑡𝑂𝐻 𝐶 [𝐸𝑡𝑂𝐻] * 𝐾 𝐴4 = * [𝐷𝐸𝐶] 𝐶 𝐷𝐸𝐶 𝐾 𝐴5 = * [𝐻 2 𝑂] 𝐶 𝐻2𝑂 𝑟 𝐴 = 𝑟 3 = 𝑘 3 𝐸𝑡𝑂𝐻 2 𝐶𝑂2 -𝑘 -3 𝐷𝐸𝐶 𝐻2𝑂 * 𝑟 𝐴 = 𝑘 𝐴 [𝐸𝑡𝑂𝐻] 2 𝑃 𝐶𝑂2 𝐶 2 𝑃 - [𝐷𝐸𝐶][𝐻 2 𝑂] 𝐾 𝑒𝑞 𝐶 2 1 + 𝐾 𝐴 𝑃 𝐶𝑂2 𝑃 + 𝐾 𝐴2 [𝐸𝑡𝑂𝐻] 𝐶 + [𝐷𝐸𝐶] 𝐶 𝐾 𝐴4 + [𝐻 2 𝑂] 𝐶 𝐾 𝐴5 3 𝑟 𝐵 = 𝑘 𝐵 [𝐸𝑡𝑂𝐻] 2 𝑃 𝐶𝑂2 𝐶 2 𝑃 - [𝐷𝐸𝐶][𝐻 2 𝑂] 𝐾 𝑒𝑞 𝐶 2 [𝐸𝑡𝑂𝐻] 𝐶 1 + 𝐾 𝐵 [𝐸𝑡𝑂𝐻] 𝐶 + [𝐷𝐸𝐶][𝐻 2 𝑂] [𝐸𝑡𝑂𝐻]𝐶 𝐾 𝐵3 𝐾 𝐵 𝑟 𝐶 = 𝑘 𝐶 [𝐸𝑡𝑂𝐻] 2 𝑃 𝐶𝑂2 𝐶 2 𝑃 - [𝐷𝐸𝐶][𝐻 2 𝑂] 𝐾 𝑒𝑞 𝐶 2 1 + 𝐾 𝐶 𝑃 𝐶𝑂2 𝑃 + 𝐾 𝐶2 [𝐸𝑡𝑂𝐻] 𝐶 + [𝐷𝐸𝐶] 𝐶 𝐾 𝐶4 + [𝐻 2 𝑂] 𝐶 𝐾 𝐶5 2 15
Eq 22 Eq 23

Eq 24 corresponds to the rate constant, which is a function of the temperature following an Arrhenius equation, where represents the pre-exponential factor, is the activation energy, is the ideal gas constant and is the temperature.

Eq 25

The reaction rate depends on the concentration of DEC (or PC) as described in Eq 26:

Eq 26 Differential equations were solved in Matlab, using a method based on differentiation (numerical differentiation formulas, ODE15S). The objective function used is given in Eq 27. represents the number of experimental points. For the synthesis of DEC, we used 16 experiments, which represent 103 experimental points.

Eq 27

Simulation results

The kinetic parameters obtained for the synthesis of DEC and for the synthesis of PC are listed in Table 5. For the synthesis of DEC, the activation energy is around 100 kJ/mol for the four mechanisms. No value was

𝑟 𝐷 = 𝑘 𝐷 [𝐸𝑡𝑂𝐻] 2 𝑃 𝐶𝑂2 𝐶 2 𝑃 - [𝐷𝐸𝐶][𝐻 2 𝑂] 𝐾 𝑒𝑞 𝐶 2 [𝐸𝑡𝑂𝐻] 𝐶 1 + 𝐾 𝐷 𝑃 𝐶𝑂2 𝑃 +𝐾 𝐷2 [𝐸𝑡𝑂𝐻] 𝐶 + 2 [𝐷𝐸𝐶][𝐻 2 𝑂] [𝐸𝑡𝑂𝐻]𝐶 𝐾 𝐷4 2 𝑟 𝐴 𝑃𝐶 = 𝑘 𝐴 𝑃𝐶 [1,2𝑃𝑃𝐷]𝑃 𝐶𝑂2 𝐶 𝑃 - [𝑃𝐶][𝐻 2 𝑂] 𝐾 𝑒𝑞 𝐶 2 1 + 𝐾 𝐴 𝑃𝐶 𝑃 𝐶𝑂2 𝑃 + 𝐾 𝐴2 𝑃𝐶 [1,2𝑃𝑃𝐷] 𝐶 + [𝑃𝐶] 𝐶 𝐾 𝐴4 𝑃𝐶 + [𝐻 2 𝑂] 𝐶 𝐾 𝐴5 𝑃𝐶 2 𝑟 𝐵 𝑃𝐶 = 𝑘 𝐵 𝑃𝐶 [1,2𝑃𝑃𝐷]𝑃 𝐶𝑂2 𝐶 2 𝑃 - [𝑃𝐶][𝐻 2 𝑂] 𝐾 𝑒𝑞 𝐶 2 1 + 𝐾 𝐵 𝑃𝐶 [1,2𝑃𝑃𝐷] 𝐶 + [𝑃𝐶][𝐻 2 𝑂] 𝐶 2 𝐾 𝐵3 𝑃𝐶 𝑘 = 𝑘 𝑒 -𝐸 𝑎 /𝑅𝑇 𝑟 = 𝑑[𝐷𝐸𝐶] 𝑑𝑡 𝐹 𝑜𝑏𝑗 = min |[𝐷𝐸𝐶] 𝑚𝑜𝑑𝑒𝑙 -[𝐷𝐸𝐶] 𝑒𝑥𝑝 | [𝐷𝐸𝐶] 𝑒𝑥𝑝 𝑁𝑃 𝑁𝑃 𝑖=
found in the literature for the activation energy of the synthesis of DEC. The synthesis of DMC has received more scholarly attention, and the activation energies obtained with different catalysts are listed in Table 6. The value obtained in this study is near to the value obtained by Santos and colleagues and Marin and colleagues, who used commercial CeO 2 [START_REF] Marin | Kinetic and mechanistic investigations of the direct synthesis of dimethyl carbonate from carbon dioxide over ceria nanorod catalysts[END_REF][START_REF] Santos | Kinetic study for the direct synthesis of dimethyl carbonate from methanol and CO 2 over CeO 2 at high pressure conditions[END_REF]. Some researchers obtained lower activation energy by using other catalysts [START_REF] Fu | TiO 2 -Doped CeO 2 Nanorod Catalyst for Direct Conversion of CO 2 and CH 3 OH to Dimethyl Carbonate: Catalytic Performance and Kinetic Study[END_REF][START_REF] Hofmann | Direct Synthesis of Dimethyl Carbonate by Carboxylation of Methanol on Ceria-Based Mixed Oxides[END_REF][START_REF] Marin | Kinetic and mechanistic investigations of the direct synthesis of dimethyl carbonate from carbon dioxide over ceria nanorod catalysts[END_REF]. This difference is due to the composition of the catalyst. Indeed, the quantity of acid and basic sites is directly related to the catalyst activity (Tomishige et al., 2000a;[START_REF] Wang | Morphology control of ceria nanocrystals for catalytic conversion of CO 2 with methanol[END_REF] C. By increasing the degree of freedom, the regression improves. The conclusion is the same for 1,2propanediol, where the mean deviation is lower for the case of mechanism A. ). For this case, the equilibrium constant is not reached after 250 h. The elevation of the temperature has a strong impact on the kinetics. Moreover, the influence of the temperature on the thermodynamic equilibrium is very low; the concentration of DEC at the equilibrium is nearly the same for all the temperatures studied (Table 2). The use of a high temperature is an efficient solution to reduce the reaction time and to obtain a good conversion. Error! Reference source not found. represents reactions with various pressures. The fit is very good, which is mostly due to the fact that the direct experimental equilibrium was used in the kinetics. For the variation of initial concentrations of DEC and water (Figure 5), the same thermodynamic equilibrium was used for each experiment. The fit is good considering the uncertainties of the analysis of water. For reaction R16, there is no conversion because the concentration of DEC initially is higher than the concentration at the thermodynamic equilibrium. Figure 6 represents the results obtained for the synthesis of PC. In that case, the mean deviation is higher, so the fit is less good than for the case of DEC. For the thermodynamic equilibrium, there are some differences between the experimental data and the modelling. This can be due to the analysis of water in the 1,2-propanediol, which is more difficult than for ethanol. As for the case of the synthesis of DEC, the temperature has an important impact on the kinetics. Moreover, in that case, the temperature increase seems to increase the concentration of DEC at the equilibrium. It can be concluded that the model shows a reasonable fit to the experimental data considering the uncertainties of the analysis of water. The work of solving the equations was carried out for the 4 models considered. The mean standard deviations between these models and our experimental points are shown in Figure 8. First of all, we can see that for some conditions (R2, R12 and R13), whatever the model, the standard deviation is important. It is likely that in these cases, uncertainties related to the water analysis are the cause of this general shift. On the other hand, It appears that the mechanisms A and C allow better modelling of the experimental results. Mechanism B models the reactions R9, R10, R11 and R14 less well. Mechanism D is less efficient on reactions R2, R6, and R14.

Based on these findings, it is difficult to understand the origin of these discrepancies. However, we can put forward some hypotheses that further work could verify. In the A and C mechanisms, the desorption phase appears explicitly, allowing this phase to have an impact on the results of the model. The desorption phase is therefore perhaps limiting.

It also appears that the mechanisms presenting a termolecular (A,C) reaction are not discriminating in the case of this study. Assuming that the probability of occurrence of a termolecular reaction between adsorbed species is much more likely to occur between species within a liquid or gas, this finding is quite consistent.

Finally, from a mathematical point of view, the question of the number of estimated parameters could arise.

Indeed, the greater the number, the greater the variance of the system and could allow a better identification of the parameters. However, in our case, the C mechanism, with 5 parameters, is not more efficient than the A mechanism with 4 parameters.

Conclusions

This article reports the first work on the development of a kinetic model for the direct synthesis of DEC and PC from alcohol and CO 2 . A parametric study was performed using CeO 2 as a catalyst. The influences of temperature, pressure and initial concentrations of water and DEC were studied. Equilibrium constants were experimentally calculated for some experiments. Standard enthalpies and entropies of the reaction of -9.4 kJ/mol and -153 J/mol/K for the synthesis of DEC and -17.4 kJ/mol and -101 J/mol/K for PC were obtained. A difference was found between these values and the value obtained with the thermodynamic data taken from the literature. This difference can be attributed to the uncertainties of the experiments and to the uncertainties of the literature data. Indeed, several values were found for the enthalpy of formation or entropy of several compounds.

Four reaction rate models were developed, based on different mechanisms for the synthesis of DEC, and two reaction rate models were developed for the synthesis of PC. The lower mean deviation between the experimental data and the modelling is obtained for the rate law based on the Langmuir-Hinshelwood mechanism for both cases. This difference is probably due to the higher number of degrees of freedom in the case of the Langmuir-Hinshelwood mechanism. An activation energy of about 100 kJ/mol for the synthesis of DEC was found, which is similar to the results obtained in the literature for the synthesis of DMC. For the synthesis of PC, the activation energy found is lower (77 and 86 kJ/mol). Good fittings with low mean deviations were obtained between the modelling and the experimental data for the case of the synthesis of DEC. For the synthesis of PC, the mean deviations are higher, but they remain under 10 %, which gives a reasonable fit when considering the uncertainties in the analysis of water. This work on the determination of the thermodynamic equilibrium and the development of the kinetics of these two reactions will be useful for the research of new processes.

Figure 2 .

 2 Figure 2. Determination of reaction enthalpy and entropy by plotting ln Keq against the inverse of temperature, for the synthesis of PC

Figure 3 :

 3 Figure 3 : Mechanisms used to develop rate laws for the synthesis of DEC

Figure 4 :

 4 Figure 4 : Experimental DEC concentration during the time (points) and modelling with mechanism A (curves)for reactions with various temperatures (R1-R8)

Figure 5 :Figure 6 :

 56 Figure 5 : Experimental DEC concentration during the time (points) and modelling with mechanism A (curves)for reactions with various pressures (R1, R9-R11)

Figure 8 .

 8 Figure 8. Comparison of standard deviation between the 4 models and our experimental data.

Table 1 .

 1 Experimental conditions for reactions of carbonation of ethanol or 1,2-propanediol with 2g of CeO 2

					O
	CO 2	+	OH	OH	O	O	+	H 2 O
			1,2-Propanediol
					PC

Table 2 .

 2 Experimental equilibrium constants for the four groups of reactions Experimental equilibrium constants are reported in Table

	Eq 8

Table 4 .

 4 Estimation of the enthalpy and entropy of the reaction for the experimental results and the data of[START_REF] Leino | Enhanced yields of diethyl carbonate via one-pot synthesis from ethanol, carbon dioxide and butylene oxide over cerium (IV) oxide[END_REF] Shukla et al. 2018 As we can see in Table4, the enthalpy and the entropy estimated in this work are less negative than those determined with the data of Leino and colleagues 2011 and Shukla and colleagues 2018. There are several reasons for this difference. Only four experimental data sets were used to calculate these parameters, and the uncertainties concerning these experiments are high in comparison with the calculation. The calculation made to

	y=1131.5x-18.376
	R

Table 5 .

 5 . For 1,2-propanediol, the activation energy is lower, at 77 and 86 kJ/mol for the two different mechanisms. No data were found in the existing literature for the activation energy of the synthesis of cyclic carbonates. Pre-exponential factors are in the same order of 10 8 and 10 11 mol/L/h. For each mechanism, this factor corresponds to a product of different equilibrium constants, so it is difficult to compare one to another. Equilibrium constants are different from one to another, they were determined by the modelling but they cannot be validated by experimental measurements of adsorption constants. Kinetic parameters optimised from the experiments for the synthesis of DEC (R1 to R16) and PC (R17 to R23). Ka CO2 and Ka EtOH : adsorption constant of CO 2 and ethanol on the catalyst. Kf DEC-PC : constant of formation of DEC or PC. Kd DEC-PC and Kd H2O : desorption of DEC, PC and water. MD: mean deviation

			k 0	Ea	Ka CO2	Ka EtOH	Kf DEC-PC Kd DEC-PC	Kd H2O	MD
	Mechanism
			mol/L/h	kJ/mol	-	-	-	-	-	%
		Name	k 0A	Ea A	K A1	K A2		K A4	K A5
	A	Value 3.61•10 10	101	0.096	0.051		0.028	0.014	4.22%
		Name	k 0B	Ea B		K B1	K B3
	B	Value 1.39•10 8	100		0.029	0.0025		7.73%
		Name	k 0C	Ea C	K C1	K 2C		K C4	K C5
	C	Value 1.17•10 12	104	2.14	5.26		0.001	0.0005	4.25%
		Name	k 0D	Ea D	K D1	K D2	K D4
	D	Value 7.56•10 9	97.8	0.128	0.423	1.33		7.41%
	A PC	Name Value 5.78•10 9 k 0A	Ea A 77.2	K A1 1.491	K A2 9.751		K A4 0.0484	K A5 1.794	7.20%
	B PC	Name Value 5.99•10 7 k 0B	Ea B 86.2		K B1 2.059	K B3 89.6		9.41%

Table 6 .

 6 List of activation energies obtained in the literature for the synthesis of DMC Kinetic models based on the Langmuir-Hinshelwood and C mechanisms have the lowest mean deviations. This improved fit can be due to the fact that the quantity of rate constants is higher in the case of mechanisms A and

= 0.9755

ACKNOWLEDGEMENTS

The authors thank ADEME and MADNESS project for financial support. The MADNESS project has been funded with the support from the European Union with the European Regional Development Fund (ERDF) and from the Regional Council of Normandie.


Léa Kervella

Paul Berveiller

Marie Bourdillon

PhD Anne Rousseau
email: anne.rousseau@uvsq.fr

Midwives' practices related to cervical cancer screening during pregnancy: A vignette-based study

Keywords: cervical cancer, Pap smear, quality of practices, pregnancy

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

Introduction

The World Health Organization reports that cervical cancer was the fourth most common cancer among women worldwide in 2018, accounting for 311,365 deaths [1]. That year, Europe had 61,072 new cases and 25,829 deaths. In France, cervical cancer is the 12 th leading cause of cancer and ranks 10 th in causes of cancer mortality in women with about 3000 new cases and 1100 deaths yearly [START_REF] Defossez | Estimations nationales de l'incidence et de la mortalité par cancer en France métropolitaine entre 1990 et 2018. Étude à partir des registres des cancers du réseau Francim[END_REF]. These cases and deaths may be due the number of women who do not undergo cervical cancer screening (CCS) by Pap tests. In 2018, the coverage rate for this screening remained stable at 60% among women aged 25-65 [START_REF] Defossez | Estimations nationales de l'incidence et de la mortalité par cancer en France métropolitaine entre 1990 et 2018. Étude à partir des registres des cancers du réseau Francim[END_REF]. Studies have nonetheless shown that when CCS programmes are introduced into communities, marked reductions in cervical cancer incidence follow [START_REF] Gustafsson | International incidence rates of invasive cervical cancer after introduction of cytological screening[END_REF][START_REF] Andrae | Screening and cervical cancer cure: population based cohort study[END_REF].

There is no consensus among either international guidelines or European national screening programmes about the details of screening, and implementing their algorithms remains complex [START_REF]Committee on Practice Bulletins-Gynecology. Practice Bulletin No. 168: Cervical Cancer Screening and Prevention[END_REF][START_REF] Us Preventive | Screening for Cervical Cancer: US Preventive Services Task Force Recommendation Statement[END_REF][START_REF] Sawaya | Cervical Cancer Screening: More Choices in 2019[END_REF][START_REF] Hortlund | Cervical cancer screening in Sweden 2014-2016[END_REF][START_REF] Elfström | Cervical cancer screening in Europe: Quality assurance and organisation of programmes[END_REF]. Thus, the age for screening initiation varies between countries from 20 to 25 years; it is 25 years in France. The screening interval varies from 1 to 5 years depending on country and age group. In France the recommended interval for women (25-65) is 3 years, after 2 normal smears one year apart. Before 2018, there was no national organised screening programme in France. There were guidelines and some organised campaigns within different districts (including Paris). Individual CCS is covered by the national health insurance fund. It is performed by gynaecologist-obstetricians, general practitioners, or midwives, in public or private hospitals, but also in the professionals' own offices. These practitioners can work independently and/or in a hospital. Independent midwives can work in a single or multiprofessional office, either alone or with several others. Both independent and hospital midwives are legally authorised to perform Pap tests during both gynaecological preventive care and during pregnancy monitoring. Hospital midwives handle gynaecological and prenatal consultations there, under the supervision of midwife managers.One way to overcome the lack of national organised CCS would be to take advantage of prenatal consultations to screen those women who receive suboptimal or no gynaecological care except during pregnancy [START_REF] Hunter | Cervical neoplasia in pregnancy. Part 1: screening and management of preinvasive disease[END_REF][START_REF] Kuczborska | Secondary cervical cancer prevention in routine prenatal care -coverage, results and lessons for the future[END_REF]. Some studies report inconsistent results about the relevance of screening during pregnancy, given the possible increase in false positives during that period due to basal layer hyperplasia and cervical inflammation or misdiagnoses due to glandular hyperplasia of the cervical mucosa, active proliferation of basal cells, or irregular cell morphology [START_REF] Hunter | Cervical neoplasia in pregnancy. Part 1: screening and management of preinvasive disease[END_REF][START_REF] Selleret | Precancerous cervical lesions during pregnancy: diagnostic and treatment[END_REF][START_REF] Suzuki | Comparing Papanicolaou test results obtained during pregnancy and post-partum[END_REF][START_REF] Morimura | Cervical cytology during pregnancy--comparison with non-pregnant women and management of pregnant women with abnormal cytology[END_REF]. Nonetheless, the Pap test appears to be equally accurate in pregnant and non-pregnant women when performed by experienced pathologists [START_REF] Stonehocker | Cervical cancer screening in pregnancy[END_REF][START_REF] Morice | Gynaecological cancers in pregnancy[END_REF]. As international guidelines do not mention specific recommendations for pregnancy, there is no reason to think that CCS guidelines differ for pregnant and non-pregnant women [START_REF] Stonehocker | Cervical cancer screening in pregnancy[END_REF]. Guidelines in France have been mainly drafted by obstetrician-gynaecologists, although with the participation of midwives over the past several years. Guidelines issued in 2007 by the French College of Gynaecologists and Obstetricians (CNGOF) state, without distinction by gestational age, that "prenatal consultations, practised in all women of all backgrounds, should be used to perform Pap tests, if they were performed more than two years earlier" [START_REF]Prevention of cervical cancer. Guidelines[END_REF]. The Haute Autorité de Santé (HAS) guidelines [START_REF]Dépistage et prévention du cancer du col de l'utérus[END_REF] published in 2013 contradict those of CNGOF slightly, thus confusing and complicating the algorithm: they recommend offering a Pap test during the first prenatal examination and up to 14 weeks of gestation (because of the higher risk of false positives thereafter) to all women aged 25 years or older whose last test took place at least 3 years earlier. They also specify that a Pap test should be offered during pregnancy, "if possible" before the 14th week of gestation, to women with "irregular medical care" or for whom there is "little chance that they will come back after childbirth". For all others (i.e., those with regular medical care, and thus highly likely to return for consultation after childbirth), testing that could not be performed before this term will be postponed to the postnatal period (at least 8 weeks postpartum). Thus, the eligibility of women for screening remains complex, especially after 14 weeks of gestation. This ambiguity and the fear of Pap tests during pregnancy may result in under-screening women during this period. A retrospective French cohort study of 300 women from two centres showed in 2014 that the screening of eligible pregnant women was still insufficient (around 50%) [START_REF] Saulneron | Evaluation of French practices regarding cytologic cervical cancer screening during pregnancy: A bicentric retrospective cohort study[END_REF].

It therefore seemed important to us to evaluate the extent to which these guidelines are accepted and understood by midwives, who provide prenatal care during pregnancy and are therefore required to perform cervical cancer screening in France. Pregnancy monitoring (prenatal care) in France can be performed by an obstetrician gynaecologist, a general practitioner, or a midwife, in a public or private hospital, but also in the professionals' own office. It should comprise a consultation before 10 weeks, a second consultation before 15 weeks, and then monthly visits.

The main objective of the study was to describe midwives' practices regarding CCS and their understanding of women's eligibility for this screening during pregnancy.

Methods

Study design

This descriptive cross-sectional study using case-vignettes took place online, where it was available for eligible midwives to complete from 1 February to 31 May, 2018.

Study population

The survey included independent and hospital midwives who provide prenatal care and monitor women during pregnancy and work in the Ile de France region, that is, the city of Paris and the 7 administrative districts surrounding it. To select midwives in this area, an e-mail was sent to all independent midwives with offices in the region and to the midwife managers responsible for supervising the midwives who conduct prenatal consultations in hospitals. Other health professionals (gynaecologist-obstetricians, and general practitioners) and midwives who did not perform prenatal care were excluded.

Survey instrument

The self-reported questionnaire was developed by the co-authors and took into account the ambiguity of the French guidelines. It was structured in two parts. The first comprised a progressive clinical vignette in three steps (Appendix 1). Clinical vignettes describe particular clinical situations pragmatically and make it possible to question professionals about how they would deal with a concrete realistic situation; they constitute a validated tool for evaluating professional practices [START_REF] Peabody | Comparison of vignettes, standardized patients, and chart abstraction: a prospective validation study of 3 methods for measuring quality[END_REF][START_REF] Peabody | Measuring the quality of physician practice by using clinical vignettes: a prospective validation study[END_REF]. In a first step, the vignette presented the case of a woman eligible for screening: consultation at 25 weeks of gestation of a 26-year-old nulliparous primigravida, with no regular gynaecological care or cancer screening and irregular prenatal visits. Then, in step 2, the vignette varied her eligibility by the term of pregnancy (10 weeks, thus eligible in Ten midwives pretested the questionnaire before it was put online. An online questionnaire was created to enable computerized, anonymous responses.

The link to the online study was distributed by email. The National Council of the Order of Midwives furnished the email addresses of independent midwives in the Ile de France region, while those working in hospitals received the link from the midwife manager at their hospital.

Analysis

The online questionnaire produced computerized responses in an Excel document. Two coauthors (LK and MB) conducted the content analysis of the open-ended questions and classified responses by themes. Midwives' demographic and clinical practice characteristics were described and presented as frequencies and percentages. Analysis was conducted with R statistical software, version 3.3.3.

Results

Description

Of the 300 questionnaires completed by midwives in the Paris area, the 273 from midwives providing prenatal care were selected for analysis (Figure 1: Flow Chart). Table 1, which describes the midwives' characteristics, shows that the participants were mainly women, and most worked only in hospitals.

Most midwives (n=174, 63.7%) reported they would perform a Pap test for women aged 25 years, while 90 (33%) would perform it for 22-year-olds. Only 138 (50.5%) would adhere to the recommended intervals between the different tests, i.e., the first two at a one-year interval and then every 3 years (Figure 2). In total, 110 (40%) midwives adhered to the entire screening protocol (age at initiation and interval).

Among the participating midwives, 29% reported they "often" perform Pap tests during pregnancy, 55% "sometimes" and 15% "never". When they stated that they do it "often", they explained it as an activity mainly at consultations at the beginning of pregnancy with women who did not see a gynaecologist regularly.

Midwives' practices for Pap tests for women during pregnancy

As Figure 3 shows, midwives did not always choose to screen eligible pregnant women, particularly those past 14 weeks of gestation who did not see a gynaecologist except when pregnant. Only 29% of midwives would offer immediate screening at the 25-week consultation to a woman with irregular gynaecological visits, whereas 91% would offer it to a similar woman at 10 weeks. The figure shows the variations in the determination of eligibility for Pap tests directly related to gestational age (25 versus 10 weeks of gestation).

Midwives' concerns about Pap tests during pregnancy

Most midwives(78%) reported they were "very comfortable" with Pap tests during pregnancy.

Figure 4 describes their concerns about these tests during this period, summarising their opinions of technical comfort, risk to the pregnancy, and result reliability. Only 15% of midwives (n=41) considered the test technically more difficult to perform during pregnancy, mainly because of "bleeding due to the sampling", "difficulties with cervical exposure", and the "collection of endocervical cells". A still higher majority -87% (n=238) -considered that a Pap smear is safe during pregnancy. Finally, 41% of midwives (n=112) felt that the Pap test is less reliable during pregnancy, noting mainly "the smear is uninterpretable" (n=95) and "there are more false positives" (n=17).

Discussion

Main Findings

Our study showed variations in cervical cancer screening by midwives in general and during pregnancy, related to gestational age. Of 273 midwives, 174 (63.7%) reported they would do a first test for a woman aged 25 years, 138 (51%) complied with the recommended intervals between tests, and 110 (40%) adhered to the complete screening protocol (age at screening and intervals). Furthermore, for the same clinical case of an eligible pregnant woman, 29% of midwives reported they would do a Pap test when the woman was at 25 weeks of gestation, compared with 91% at 10 weeks.

Strengths and limitations

The main strength of our study was the sample size, i.e., 8% of the midwives in the Paris region (n=3492) [START_REF] Ondps | Les sagesfemmes[END_REF], although probably a higher percentage of those providing prenatal care as it is impossible to know how many midwives in the region provide this care and all of our sample did. The digital format of the questionnaire and the use of clinical vignettes enabled a quick, simple response to the questionnaire and responses that were as close as possible to current midwifery practices.

The study, nonetheless, has some limitations. First there is a selection bias: midwives who participated were undoubtedly more interested in the subject and probably more aware of it than those who did not respond. There is also a social desirability bias: the tool does not allow an assessment of the actual practices of midwives but rather their self-reported hypothetical practices. We nonetheless observed variations in practices, which may be underestimated due to these biases.

Another limitation was due to the method of survey distribution: we cannot know how many midwives were invited to participate and eligible responded because we did not know the number of midwives performing prenatal consultations, nor the number of midwives to whom the supervising midwives sent the survey link.

Interpretation

In our sample, 51% of midwives adhered to the recommended interval between screenings in France (the first two at one-year intervals and then every three years), but 26% performed it too frequently. The complete screening protocol (age at initiation and interval) was followed by 110 (40%) midwives. These rates are consistent with those from international studies [START_REF] Boone | Discontent and Confusion: Primary Care Providers' Opinions and Understanding of Current Cervical Cancer Screening Recommendations[END_REF][START_REF] Teoh | Adherence to the 2012 national cervical cancer screening guidelines: a pilot study[END_REF][START_REF] Perkins | Challenges in cervical cancer prevention: a survey of U.S. obstetrician-gynecologists[END_REF][START_REF] Berkowitz | Cervical cancer screening intervals, 2006 to 2009: moving beyond annual testing[END_REF].

In view of the lack of consensus about the various guidelines between and sometimes within countries, variations in practices leading to overscreening have been observed. In a US study [START_REF] Perkins | Challenges in cervical cancer prevention: a survey of U.S. obstetrician-gynecologists[END_REF], fewer than 20% of practitioners followed all the recommendations related to age at screening initiation, age-specific screening intervals, and screening discontinuation. In other studies from the USA, the factors most frequently reported for non-adherence were the provider's sex, specialty, and lack of knowledge of the guidelines, as well as the woman's request for a different screening interval [START_REF] Teoh | Adherence to the 2012 national cervical cancer screening guidelines: a pilot study[END_REF][START_REF] Becerra-Culqui | Patterns and correlates of cervical cancer screening initiation in a large integrated health care system[END_REF]. We did not study the reasons for nonadherence, but further investigation of this topic seems essential for improving both adherence and screening.

Our results about the number of women eligible for screening during pregnancy are consistent with those of the 2014 two-center cohort study evaluating the practice of CCS during pregnancy, which showed that only 26.9% of the eligible women were screened at that time [START_REF] Peabody | Comparison of vignettes, standardized patients, and chart abstraction: a prospective validation study of 3 methods for measuring quality[END_REF]. Our results also revealed variations in midwives' professional practices regarding screening eligibility according to gestational age. These variations may be associated with difficulty in absorbing and understanding the nuances between the different sets of recommendations and with the formulation of the HAS recommendations, which remains quite complex and therefore might complicate decision-making. As screening guidelines become more complex, adherence to them becomes more difficult. Midwives are forced to pick and choose from differing recommendations that use ambiguous terms such as "if possible".

A national screening programme, launched in October 2018, should also improve screening coverage. Recently, after the completion of our study, in response to insufficient screening utilisation rate, the HAS recommended that HPV testing be performed every 5 years, consistent with most international recommendations [START_REF]Committee on Practice Bulletins-Gynecology. Practice Bulletin No. 168: Cervical Cancer Screening and Prevention[END_REF][START_REF] Elfström | Cervical cancer screening in Europe: Quality assurance and organisation of programmes[END_REF][START_REF] Becerra-Culqui | Patterns and correlates of cervical cancer screening initiation in a large integrated health care system[END_REF][START_REF]Évaluation de la recherche des papillomavirus humains (HPV)[END_REF]. Moreover, this test can now be performed by self-sampling, which should contribute to better screening coverage.

Lastly, women are also seeking information about Pap smears for CCS; some studies highlight women's lack of information about cervical cancer and its prevention [START_REF] Kola-Palmer | Awareness and knowledge of human papilloma virus in UK women aged 25 years and over: Results from a cross-sectional internet-based survey[END_REF][START_REF] Wafo | Evolution of the awareness of Human Papillomavirus (HPV) in the French population: Results of a telephonic inquiry[END_REF]. Information for women is therefore one of the levers for improving screening coverage outside pregnancy.

Conclusion

Pregnancy is an appropriate time to screen women who meet the criteria for CCS but who have not had it, especially those not receiving regular gynaecological care. Midwives have an important role to play in this screening during prenatal consultations. The objective of screening during pregnancy is to correct the screening and not to provide immediate active management.

Clear guidelines on screening during pregnancy would likely reduce variations in practice during this period. Moreover, standardising the guidelines would remove the ambiguity and probably increase the screening rate.

  any situation) and by her regularity of gynaecological follow-up in step 3 (regular follow-up, therefore not eligible at 25 weeks). At the end of each of the three steps of this vignette, participants were asked to choose one action among four possible answers: -Perform a Pap test during the consultation, -Offer to perform a Pap test at the postnatal visit, -Refer the woman to a gynaecologist-obstetrician for screening, -Do not mention CCS at the consultation. The second part of the self-administered questionnaire used multiple-choice closed-ended questions and open-ended questions. It asked participants about their practices, opinions, and concerns about the performance of Pap tests: age range and exam interval that they applied in their practice, their frequency during prenatal consultations, midwives' sense of comfort with performing Pap smears, fear of risks to pregnancy, and the reliability of Pap test results during pregnancy. Finally, questions collected some information about the participants: gender, age, experience, and independent and/or hospital practice.

Figure 1 :

 1 Figure captions

Figure 2 :

 2 Figure 2: Screening protocol for Pap test reported by midwives The figure described the screening protocol for Pap test reported by midwives: screening age at initiation and screening interval.

Figure 3 :

 3 Figure 3: Midwives' practices declared for Pap tests for women during pregnancy The figure describes the practices declared by midwives for each step of the vignette.

Figure 4 :

 4 Figure 4: Midwives' concerns about Pap test during pregnancy The figure describes concerns about Pap test during pregnancy, summarising their opinions of technical comfort, risk to the pregnancy, and result reliability

Table 1 :

 1

	Midwives' characteristics
			N=273
			n (%)
	Gender	Female	264 (96.9)

This research did not receive any specific grant from funding agencies in the public, Declarat tions

Ethics statement

The National Data Protection Authority (Commission Nationale de l'Information et des Libertés) approved this study on 1 February 2018 (n° UVSQ-N-2018-005). The questionnaire was anonymous. Participants were informed about the purpose of the study from the start, and their consent to participate was tacit: they were free not to participate and not to submit the final questionnaire.

Highlights:

Practices of cervical screening during pregnancy vary according to gestational age.

Realising cervical screening during pregnancy if woman risk escaping screening.

Abstract

Objective: To describe midwives' practices related to cervical cancer screening and women's eligibility for screening during pregnancy Study design: Cross-sectional vignette-based study of French midwives during February-May, 2018.

Main outcome measures:

Participants were asked to complete an internet-based questionnaire: a clinical case-vignette about a woman eligible for cervical cancer screening during pregnancy and a short self-administered questionnaire.

Results:

We obtained 273 complete questionnaires from eligible midwives. Of those responding, 15% reported that they never screened for cervical cancer during pregnancy, 63.7% did so for women 25 years or older, and 51% adhered to the recommended intervals between tests. Overall, 110 (40%) midwives adhered to the complete screening protocol (age at initiation and interval). In this clinical case vignette of a woman meeting the criteria for screening, only 29% of midwives reported they would perform a Pap test at 25 weeks of gestation, while 91% would at 10 weeks.

Conclusion:

Midwives' practices of cervical cancer screening and their determination of women's eligibility during pregnancy vary, especially according to gestational age; Nevertheless, pregnancy is an appropriate time to screen women who meet the criteria for cervical cancer screening, especially if they are not receiving regular gynaecological care.