Y Katrib

G Deiber

P Mirabel

S Le Calvé

C George

A Mellouki

G Le Bras

Atmospheric loss processes of dimethyl and diethyl carbonate

Keywords: OH radicals, rate coefficients, uptake measurements, dimethyl carbonate, diethyl carbonate

A combined study of the OH gas phase reaction and uptake on aqueous surface of two carbonates, dimethyl and diethyl carbonate has been carried out to determine the atmospheric lifetimes of these compounds. Rate coefficients have been measured for gas phase reactions of OH radicals with dimethyl and diethyl carbonate. The experiments were carried out using pulsed laser photolysis -laser induced fluorescence over the temperature range 263-372 K and the kinetic data were used to derive the following Arrhenius expressions (in units of cm 3 molecule -1 s -1 ): for dimethyl carbonate, k1 = (0.83 ± 0.27)10 -12 exp[-(247 ± 98)/T] and for diethyl carbonate, k2 = (0.46 ± 0.15)10 -12 exp[(503 ± 203)/T]. At 298 K, the rate coefficients obtained (in units of 10 -12 cm 3 molecule -1 s -1 ) are: k1 = (0.35 ± 0.04) and k2 = (2.31 ± 0.29).

The results are discussed in terms of structure-activity relationships.

The uptake coefficients of both carbonates on aqueous surfaces were measured as a function of temperature and composition of the liquid phase, using the droplet train technique coupled to a mass spectrometric detection. Dimethyl and diethyl carbonate show very similar results. For both carbonates, the measured uptake kinetics were found to be independent of the aqueous phase composition (pure water, NaOH solutions) but dependent on gas-liquid contact time which characterises a surface saturation effect. The uptake coefficient values show a slight negative temperature dependence for both carbonates. These values vary from 1.410 -2 to 0.610 -2 in the temperature range of 265-279 K for dimethyl carbonate, from 2.410 -2 to 0.910 -2 in the temperature range of 270-279 K for diethyl carbonate. From the kinetic data, the following Henry's law constants were derived between 279 and 265 K : dimethyl carbonate, H1 = 20-106 M atm -1 ; and diethyl carbonate, H2 = 30-98 M atm -1 . The reported data show that the OH reaction is the major atmospheric loss process of these two carbonates with lifetimes of 33 and 5 days, respectively, while the wet deposition is a negligible process.

Introduction

Organic carbonates have been suggested as fuel additives because their use may reduce the vapour pressure of fuels and in turn reduce their emissions to the atmosphere by evaporation. If pure dimethyl carbonate freezes at 1°C, at a concentration of 3-4 % in gasoline, it remains in solution without becoming cloudy or hazy below -40 °C allowing it to be used as a fuel additive in winter. Organic carbonates have also a good blending octane [START_REF] Pacheco | Review of Dimethyl Carbonate (DMC) Manufacture and its Characteristics as a Fuel Additive[END_REF] and very high oxygen contents, in contrast to ethers [START_REF] Bilde | Atmospheric Chemistry of Dimethyl Carbonate : Reaction with OH Radicals, UV Spectra of CH 3 OC(O)OCH 2 and CH 3 OC(O)OCH 2 O 2 Radicals, Reactions of CH 3 OC(O)OCH 2 O 2 with NO and NO 2 , and Fate of CH 3 OC(O)OCH 2 O Radicals[END_REF], which can reduce significantly CO emissions from motor vehicles.

In addition to these primary emission sources, organic carbonates can be generated in the atmosphere during the oxidation of diethers. For instance, the oxidation of dimethoxy methane (CH3OCH2OCH3) leads to about 25 % of dimethyl carbonate (CH3OC(O)OCH3) [START_REF] Wenger | Mechanisms for the chlorine atom initiated oxidation of dimethoxymethane and 1,2-dimethoxyethane in the presence of NOx[END_REF].

Although having low toxicity, carbonates may play a significant role in photochemical pollution by contributing to the formation of tropospheric ozone and other photooxidants.

When released into the atmosphere, these oxygenated volatile organic compounds (VOCs) can undergo photochemical transformations initiated by OH radicals or be taken up by clouds, which also represent a net sink during precipitation events. By analogy with acetates, reactions with the NO3 radical (Langer et al., 1993), and with ozone (Atkinson et al., 1984), as well as photolysis [START_REF] Calvert | Photochemistry[END_REF] can be considered as slow loss processes for the carbonates. Therefore, kinetic and mechanistic information on the major tropospheric gasphase and multi-phase oxidation of organic carbonates is needed, in order to assess their impact on air quality.

In this work, we report absolute rate coefficient data for the OH radical reactions with dimethyl carbonate (k1) and diethyl carbonate (k2) over the temperature range 263- This work provides the second determination of k1 [START_REF] Bilde | Atmospheric Chemistry of Dimethyl Carbonate : Reaction with OH Radicals, UV Spectra of CH 3 OC(O)OCH 2 and CH 3 OC(O)OCH 2 O 2 Radicals, Reactions of CH 3 OC(O)OCH 2 O 2 with NO and NO 2 , and Fate of CH 3 OC(O)OCH 2 O Radicals[END_REF] and the first one for k2.

Since carbonates are polar , it is expected that they interact with atmospheric liquid water and in this context, we have determined the uptake coefficients of both carbonates by the aqueous phase. To our knowledge, these measurements are the first to be reported.

Experimental Section

OH experiments

The technique of pulsed laser photolysis -laser induced fluorescence (PLP-LIF) used in the OH experiments has been described in detail previously [START_REF] Mellouki | Kinetic studies of OH reactions with H 2 O 2 , C 3 H 8 and CH 4 using the pulsed laser photolysis -laser induced fluorescence method[END_REF][START_REF] Mellouki | Kinetics of OH radical reactions with a series of ethers[END_REF], and is only briefly discussed here. OH radicals were produced by photolysis of H2O2 at  = 248 nm (KrF excimer laser). The concentration of OH radicals was monitored at various reaction times ranging from ca. 10 s to 10 ms by pulsed laser induced fluorescence (LIF). A Nd:YAG pumped frequency doubled dye laser was used to probe the OH radical at  = 282 nm, the subsequent fluorescence was detected by a photomutiplier, fitted with a 309 nm narrow bandpass filter. The output pulse from the photomultiplier was integrated for a preset period by a gated charge integrator. Typically the fluorescence signal resulting from 100 probe laser shots was measured for 10 to 15 different delay times and averaged to generate OH concentration-time profiles over at least three lifetimes. Carbonate/H2O2 mixtures in helium diluent were flowed slowly through the cell, so that each photolysis/probe sequence interrogated a fresh gas mixture and reaction products did not build up in the cell.

All experiments were carried out under pseudo-first-order conditions with

[carbonate]  [OH]o, the initial concentration of OH being lower than 2x10 11 molecule cm -3 .

The temporal profiles of the OH concentration, therefore, followed the pseudo-first-order rate law:

[OH]t = [OH]0 e -k i 't where ki' = ki [carbonatei] + k'0 (I)
where carbonatei refers to the carbonate in reaction i (i = 1, 2) and ki is the rate coefficient for the reaction of OH with the carbonate (i). The decay rate, k' 0 , is the first-order decay of OH in the absence of the carbonate. The value of k' 0 is essentially the sum of the pseudo first order rate constant for OH with H 2 O 2 , and the rate constant for diffusion of OH out of the detection zone. The concentration of OH at various reaction times (delay between the photolysis and probe pulses) was determined by measuring the LIF signals at those delay times. Weighted least-squares analyses were used to fit the data to the above equation and extract the values of ki'. The second-order rate coefficients (ki) were obtained from the measured values of ki' at various carbonate concentrations.

Helium (UHP certified to > 99.9995 %) from Alphagas, was used without purification.

A 50 wt. % H2O2 solution was obtained from Prolabo, and was further concentrated by bubbling helium through for several days prior to use it in order to remove water, and was then constantly flushed with He during the course of the experiments. During a kinetic experiment, the gas flow was admitted into the reaction cell by passing a small flow of helium through a glass bubbler containing H2O2. Dimethyl carbonate (> 99 %) and diethyl carbonate (99 %) were respectively obtained from Fluka and BDH. They were further purified by repeated freeze-pump-thaw cycles and fractional distillation before use.

For the kinetic measurements, the carbonates were premixed with helium in a 10 L glass light-tight bulb to form a (0.7 -4.0) % mixture at a total pressure of around 750 Torr. All the gases flowed into the reactor through Teflon tubing. The gas mixture containing the carbonate, photolytic precursor (H2O2) and the bath gas were flowed through the cell with a linear velocity ranging between 1 and 3 cm s -1 . The concentrations of the carbonates were calculated from their mass flow rates, temperature and pressure in the reaction cell. All flow rates were measured with mass flowmeters calibrated by measuring the rate of pressure increase in a known volume. The pressure in the cell was measured with a capacitance manometer located at the cell entrance.

Uptake experiments

The uptake rate of a trace gas by a liquid is a multi-step process that can be related to fundamental properties of the gas, interface and the condensed phase such as the mass accommodation coefficient (), solubility and reactivity. The rate at which a trace gas molecule may be transferred into the condensed phase can be obtained from the kinetic theory of gases. This allows the calculation of the net flux net that crosses the interface:

 net c n =   1 4  (II)
where <c> is the trace gas average thermal speed,  the uptake coefficient (taking into account all processes potentially affecting the uptake rate) and n the number density of the trace gas.

Uptake rates were measured using, the droplet train technique already described elsewhere [START_REF] Magi | Investigation of the Uptake Rate of Ozone and Methyl Hydroperoxide by Water Surfaces[END_REF][START_REF] Schweitzer | Multiphase Chemistry of N 2 O 5 , ClNO 2 , and BrNO 2[END_REF]. We will therefore provide only a brief summary of its principle of operation. The uptake coefficient was determined by measuring the decrease of the gas phase concentration of the trace species, due to their exposure to a monodisperse train of droplets. These latter were generated by a vibrating orifice (100 µm diameter) leading to droplet diameters of about 200 µm. The apparatus, where the contact between both phases takes place, is a vertically aligned flowtube. Its length can be varied up to 20 cm, in order to change the gas/liquid interaction time (0 -20 ms) or the surface exposed by the droplet train (0 -0.2 cm 2 ). Since the uptake process is directly related to the total surface S exposed by the droplets, any change S in this surface results in a change of the trace gas density n at the exit ports of the flowtube. The uptake coefficient was calculated by considering the kinetic gas theory and the integrated signal during the transit time due to changes in the exposed surface [START_REF] Worsnop | Temperature dependence of mass accommodation of SO 2 and H 2 O 2 on aqueous surfaces[END_REF]:

       -    =  n n n ln S c 4F g (III)
where Fg is the carrier gas volume flow rate, n and (n-n) are respectively the trace gas density at the inlet and outlet port of the interaction chamber. The overall uptake coefficient  was derived from the measurement of the fractional changes in concentration ln[n/(n-n)] as a function of <c>S/4Fg. This parameter can be measured as a function of the total pressure, gas/liquid contact time or composition of the liquid used to produce the droplets. These last measurements are necessary to decouple the overall process into individual steps. An important aspect of this technique is the careful control of the partial pressure of water in the flowtube since it controls the surface temperature of the droplets through evaporative cooling [START_REF] Worsnop | Temperature dependence of mass accommodation of SO 2 and H 2 O 2 on aqueous surfaces[END_REF]. Therefore, the carrier gas (helium) was always saturated, at a given temperature, with water vapour before entering the flow tube.

The extraction of kinetic information from the droplet train technique may be affected by the high speed of the droplets which favors convective transport into the droplets.

However, several facts demonstrate that, given the accuracy of the experiments, this effect does not represent a significant source of error. The time scale of the experiment was short (typically less than 20 ms) which do not allow a massive influence of convective transport.

Using the description given by [START_REF] Pruppacher | Microphysics of Clouds and Precipitations[END_REF], some calculations have shown that this influence on the uptake process is less than 5% for times below 20 ms (George, 1993), in agreement with the results of [START_REF] Baboobal | A sensitivity study of a theoretical model of SO2 scavenging by water drops in air[END_REF].

Aqueous solutions used to prepare the droplets were made from Milli-Q water (18 M cm) and NaOH (BDH,  99 %) when necessary. Dimethyl carbonate ( 99 %) and diethyl carbonate (99 %) were respectively obtained from Fluka and Aldrich.

The gas stream coming out of the flowtube was analysed using a differentially pumped mass quadruple spectrometer Pfeiffer Vacuum QMS with an ionisation energy of 60 eV. The signal was averaged over a second in order to increase the signal to noise ratio. Dimethyl carbonate was monitored at 59 amu (CH3C(O)O + ) and diethyl carbonate at 63 (C + (OH)3) and 91 (C2H5OC + (OH)2) amu. In addition, H2O and an inert tracer SF6 were respectively monitored at 18 (H2O + ) amu and 89 (S + F3) amu during the experiments in order to see any potential perturbations in gas phase concentrations.

Results and Discussion

OH reactions rate constants

Loss of the OH radical in the presence of the substrate was, as expected, found to be exponential in all cases and plots of ki'-k0' versus carbonate concentration showed excellent linearity. Representative data of OH reactions with both carbonates are shown in Figure 1.

Values of k i for dimethyl and diethyl carbonate over the temperature range 263-372 K were obtained from least-squares fits of the data and are listed in Table I. The quoted errors for ki include 2 from the least-squares analysis and an estimated systematic error of 5% due to uncertainties in measured concentrations. Possible errors in the measured rate coefficients due to secondary reactions of OH with the radicals produced in reactions ( 1) and ( 2) were significantly reduced by using [carbonate]/[OH]0 ratios in the range 10 2 -10 4 .

As indicated in Table I, the determined rate coefficients were shown to be independent of carbonate concentration (from 0.5 to 49.510 14 molecule cm -3 ). The rate coefficients were also insensitive to variations in the flow velocity through the reactor (v = 1 -3 cm s -1 ), in the photolysis laser energy at 248 nm (E = 1.5 -6 mJ) and in pressure (P = 100 -300 Torr).

The temperature dependence of the rate coefficients k1 and k2 can be conveniently expressed in the conventional Arrhenius form (k = Ae -Ea/RT ) as shown in Figure 2. The conventional Arrhenius parameters derived for k1 and k2 are given in Table II along with data reported by [START_REF] Bilde | Atmospheric Chemistry of Dimethyl Carbonate : Reaction with OH Radicals, UV Spectra of CH 3 OC(O)OCH 2 and CH 3 OC(O)OCH 2 O 2 Radicals, Reactions of CH 3 OC(O)OCH 2 O 2 with NO and NO 2 , and Fate of CH 3 OC(O)OCH 2 O Radicals[END_REF] for k1 who used the Flash Photolysis-Resonance Fluorescence technique. The results are in good agreement over the entire temperature range of this study.

However, a slight curvature is clearly observed for dimethyl carbonate. This curvature in the Arrhenius plot may arises from the fact that two different reaction channels occur in the temperature range (263-372 K). At higher temperature, the OH radical reactions proceeds via H-atom abstraction from the C-H bonds similarly to the alkanes [START_REF] Atkinson | Gas-phase tropospheric chemistry of organic compounds[END_REF]. At lower temperature, a second pathway forming a long-lived adduct by OH addition to the carbonyl group may be possible. Both pathways would lead to the formation of the same products. This was, for instance, suggested for OH reactions with aliphatic ketones [START_REF] Wallington | Flash photolysis resonance fluorescence investigation of the gas-phase reactions of OH radicals with a series of aliphatic ketones over the temperature range 240-440 K[END_REF][START_REF] Wollenhaupt | Rate coefficients for Reaction of OH with acetone between 202 and 395 K[END_REF]. In the case of OH reaction with acetone, [START_REF] Wollenhaupt | Rate coefficients for Reaction of OH with acetone between 202 and 395 K[END_REF] suggest the possible formation of an association complex [(CH3)2COOH] # which can decompose at low temperatures by C-C bond fission to yield acetic acid (CH3C(O)OH) and CH3 radicals as products. Even if the change in slope in our temperature range is less marked than [START_REF] Wollenhaupt | Rate coefficients for Reaction of OH with acetone between 202 and 395 K[END_REF] found for acetone, both processes may occur. k1 could then be written as the sum of two exponentials (k1 = A1e -Ea 1 /RT +A2e -Ea 2 /RT ). Ea1/R is assumed to be equal to 1070 which corresponds to the activation energy for the reaction of ethane with OH in the temperature range of 300-390 K [START_REF] Donahue | New rate constants for ten OH alkane reactions from 300 to 400 K: an assessment of accuracy[END_REF]. This assumption is justified by the fact that both compounds have only two individual -CH3 groups which have positive temperature dependence [START_REF] Atkinson | Gas-phase tropospheric chemistry of organic compounds[END_REF]. The plot of k1=5.910 -12 exp(-1070/T) + 1.310 -14 exp(795/T) is in excellent agreement with the experimental data as it is shown in figure 2.

In contrast to k1 which has a similar positive temperature dependence than the rate constant of OH reaction with ethane in the temperature range of 300-390 K, k2 has a negative temperature dependence compared to the net positive dependence observed for the rate constant of OH reaction with n-butane. Therefore, at 400 K, OH + n-butane is faster than OH + DEC, but is slower at 250 K.

The obtained rate constant at 298 K can be compared with the calculated ones using the structure-activity relationship (SAR) [START_REF] Atkinson | A structure-activity relationship for the estimation of rate constants for the gas-phase reactions of OH radicals with organic compounds[END_REF], Kwok et al., 1995). In this method, calculation of H-atom abstraction for C-H bonds is based on the estimation of -CH3 , -CH2and -CH group rate constants, assuming that the group rate constants depend on the identity of substituents attached to the group. At 298 K, the group rate constants are given by:

k(CH3-X) = kprim F(X), k(Y-CH2-X) = ksec F(X) F (Y), k((Y)(Z)CH(X)) = ktert F(X) F(Y) F(Z)
, where kprim, ksec, ktert are the rate constants per CH3-, -CH2-, CHgroups and F(X), F(Y), F(Z) are the substituent factors. k1 and k2 have been calculated using the following parameters at 298 K (Kwok et al., 1995): kprim = 0.136 x 10 -12 , ksec = 0.934 x 10 -12 (units of cm 3 molecule -1 s -1 ), F(-CH3) = 1, F(-CH2-) = 1.23, F(-OC(O)OR) is not defined but was assumed to be equal to F(-OC(O)R) = 1.6. The calculated values of k1 and k2 using these parameters were higher than the experimental ones (the calculated values are in parentheses): k1 = 0.35 (0.44) and k2 = 2.3 (3.3) (in 10 -12 cm 3 molecule -1 s -1 ). A better agreement between the experimental and calculated rate constants is obtained with a new substituent factor for the -OC(O)OR group: F(-OC(O)OR) = 1.17, derived from the experimental rate coefficient of OH reaction with dimethyl carbonate and diethyl carbonate.

Uptake experiments

As already mentioned, uptake coefficients are measured from the fractional changes in trace gas concentration due to a modification in the exposed droplets surface (equation III)

which is function of diffusion rates in both phases, mass accommodation process, and solubility and reactivity in the liquid phase. To each of these processes, one can attribute a specific uptake coefficient and the overall uptake coefficient is calculated by summing up the individual resistances (defined as the inverse of the specific uptake coefficient) according to [START_REF] Kolb | Laboratory Studies of Atmospheric Heterogeneous Chemistry[END_REF] :

1 1 1 1 1 2 1        = + + + -+ +   +       - diff sat rxn = < c > d eff 8D g c 4HRT D a 2 t k 1 (IV)
where deff is the effective droplet diameter (which takes into account the fact that a droplet train may not be considered as a sum of individual droplets; note however that its value is very close to the real diameter) [START_REF] Worsnop | Temperature dependence of mass accommodation of SO 2 and H 2 O 2 on aqueous surfaces[END_REF], H the Henry's law constant, R the perfect gas constant, T the droplets temperature, Dg and Da the gas and aqueous phase diffusion coefficients respectively, t the gas / liquid contact time and k the first order rate constant for a given reaction in the liquid phase. The term -1/2 accounts for the distortion of the Boltzmann collision rate.

This relation clearly shows that the uptake coefficient is a function of different fundamental properties of the gas molecule such as its solubility, diffusion, etc. The treatment used to obtain equation (IV) is very similar to the one used for the calculation of deposition velocity on the ocean surface [START_REF] Liss | Flux of Gases across the Air-Sea Interface[END_REF].

The observed curvature in figure 3 characterises the existence of a surface saturation effect. This is confirmed by figure 4 which shows the inverse of uptake coefficient as a function of the gas/liquid contact time for dimethyl carbonate. It can be clearly seen that  is time dependent, which means that saturation of the droplets' surface occurs in the temperature range studied here (265-279 K). The uptake coefficients were therefore determined by using the first straight data. The quoted errors for  include then a large estimated error of 10 % and 2 from the least-squares analysis.

On the other hand, uptake coefficients are independent of the aqueous phase composition. Indeed, we observed the same results when the uptake was studied over pure water and a 0.1M NaOH solution. From this observation, we concluded that the uptake coefficient on liquid droplets are controlled by gas diffusion diff, mass accommodation  and aqueous phase saturation, i.e. equation V can be simplified to:

a D 8HRT πt c α 1 2 1 g 8D eff d > c < γ 1   + + - = (V)
Equation V may also be written as:

γ corr 1 a D 8HRT πt c α 1 diff γ 1 γ 1 =   + = - (VI)
The gas phase diffusion coefficients (Dg) are not known and therefore had to be estimated, as already mentioned, by the method presented by [START_REF] Reid | The properties of gases and liquids[END_REF]. In addition, since our carrier gas is a mixture of helium and water vapour, it was necessary to compute the diffusion coefficient in this background. This was done according to the following equation: where PH2O and PHe are the partial pressures of water and helium respectively, Dg-H2O and Dg-He are the binary diffusion coefficients of the trace gases in water and helium respectively (see Table III for numerical values).

The raw data (1/) were corrected for gas phase diffusion according to equation VI recommended by [START_REF] Kolb | Laboratory Studies of Atmospheric Heterogeneous Chemistry[END_REF]. The Fuchs-Sutugin equation [START_REF] Fuchs | Highly dispersed aerosols[END_REF]) is certainly the most widely employed for the description of mass transport in the Knudsen transition regime (0.1 < Kn < 1), which is our case. However, its derivation is less simple and the observed deviation, compared to Kolb's equation, is less than 5% for our experimental conditions (even less than 3% for some experiments) [START_REF] Kolb | Comment on Mathematical-Models of the Uptake of Clono2 and Other Cases by Atmospheric Aerosols[END_REF]. The error due to this approximation can be included in the given error of 2 ± 10 %.

In this work, carbonate concentrations varied typically between 10 and 100 ppmv. Both carbonates show very similar results. For dimethyl carbonate and diethyl carbonate, the uptake coefficients  decrease respectively from 1.410 -2 to 0.610 -2 between 265 and 279 K and from 2.410 -2 to 0.910 -2 M atm -1 between 270 and 279 K, for the different aqueous solutions (Figure 5). The raw uptake coefficients  and the corrected ones corr are listed in Table IV and Table V for both carbonates in function of the experimental conditions.

By plotting 1/ versus t 1/2 , the Henry's law constant H and the mass accommodation  can be respectively extracted from the slope and the intercept according to equation (V). Mass accommodation coefficients  have been determined for dimethyl carbonate and for diethyl carbonate. Their values decrease from 0.2 to 0.01 between 265 and 279 K for both carbonates for the different aqueous solutions as shown in Figure 6. As shown in Figure 4, the intercepts are very small (i.e., the mass accommodation coefficients are in fact very large) and therefore introduces large errors bars. It must also be underlined that the errors stated above are just statistical errors, which do not account for other error sources such as the uncertainties in the values of the gas phase diffusion coefficient. As we have seen above, the latter is estimated by the [START_REF] Reid | The properties of gases and liquids[END_REF] method (equation VII), which generally leads to an average error of 9% when compared to experimental values. However, in some occasions the error can reach 30%.

Interfacial transport is characterised by the mass accommodation coefficient . To explain the negative temperature dependence of  , [START_REF] Nathanson | Dynamics and Kinetics at the Gas-Liquid Interface[END_REF] developed a model suggesting that the gas uptake proceeds via growth of critical clusters containing N* molecules. The incoming gas molecule strikes the surface and becomes a loosely bound surface specie (Asurf) which participates in the nucleation process. If such a molecule becomes part of a critical sized cluster, it will invariably be incorporated into the bulk liquid via aggregation growth. This process can be represented as:

(VIII)

where g, surf and aq represent the gaseous, surface and liquid state of the studied specie.

A*surf represents the specie within a critical cluster.

It is possible to express the mass accommodation  as follows:

          - =         -           - = = - RT ΔG exp RT ΔG exp RT * ΔG exp k k α 1 α obs vap désorb sol (IX)
where G * and Gvap are the free energies of the vapour and the critical cluster compared to the free energy of surface state. The values for Hobs and Sobs can be obtained by plotting ln(/(1-)) as a function of 1/T. The slope of such a plot is -Hobs/R and the intercept is Sobs/R. The obtained values on water are reported in Table VI.

Using the classical nucleation theory, it is possible to link the thermodynamic parameters Hobs and Sobs to the critical cluster size N*, representing the minimum value for efficient incorporation [START_REF] Nathanson | Dynamics and Kinetics at the Gas-Liquid Interface[END_REF]:

( ) (
)

) M kcal ( 10 1 , 0 1 N 53 , 7 1 N 10 H 1 3 / 2 * * obs -  - -  + -  - =  (X) ( ) ( ) (
)

) K M cal ( 13 1 , 0 1 N 21 , 9 1 N 19 1 N 13 S 1 1 3 / 2 * * * obs - -  - -  + -  - -  - =  (XI)
The N* values calculated for dimethyl and diethyl carbonate are respectively 4.4 and 5.6. The fact that those values are not integer might be due to the influence of the orientation of the molecule at the interface, related to the impact angle. Our results are in very good agreement with the theoretical N* values and the experimental results given by [START_REF] Nathanson | Dynamics and Kinetics at the Gas-Liquid Interface[END_REF] or by our group as it is shown in figures 7a and 7b.

In this model, the facility of incorporation of a molecule in the condensed phase depends on its capacity to participate to the nucleation phenomenon. This capacity should be directly related to the specific structure of the molecule. It has been demonstrated that the critical cluster size will be smaller when the capacity to make hydrogen bonds is important as it is well known for alcohols or carboxylic acids. In contrast to these families, the N* values for organic carbonates determined in this work are much larger in correlation with their low capacities to make hydrogen bonds. The chemical structures of dimethyl and diethyl carbonate are similar, at least for the functional group, and this is probably why very few differences are observed in the N* values. According to the model, once a critical cluster is formed around the hydrophilic part (-OC(O)O-) of the carbonate, the cluster continues to grow irreversibly.

The deduced Henry's law constants are plotted as a function of temperature in Figure 8 for both carbonates. For dimethyl carbonate and diethyl carbonate, the measured H values decrease respectively from 106 to 20 M atm -1 between 265 and 279 K and from 98 to 30 M atm -1 between 270 and 279 K, for the different aqueous solutions. It is important to underline again that any small errors (experimental errors or systematic errors due, for example, to incorrect estimates of the diffusion coefficients in both phases) will in turn modify the calculated Henry's law constant. Unfortunately, these Henry's law constants could not be calculated using a predictive method (Meylan et al., 1991) because the authors do not take into account the carbonate structure.

Our experimental data can be expressed as a function of the temperature according to the expression:

T B A H log + = (XII)
The obtained fitted data in figure 8 are A= -8.0 ± 3.8, B= 2600 ± 1000 for dimethyl carbonate and A= -10.2 ± 2.9, B= 3280 ± 800 for diethyl carbonate.

The Henry's law constants for both carbonates can be extrapolated at 298 K from the above expression leading to: H1 (298 K) = 5.3 ± 1.7 M atm -1 (dimethyl carbonate) and H2

(298 K) = 6.3 ± 1.5 M atm -1 (diethyl carbonate). These values for carbonates (ROC(O)OR) are smaller than those of the corresponding ketones (RC(O)R): H (298 K) = 30 M atm -1 (acetone) [START_REF] Staudinger | A critical review of Henry's law constants fir environmental applications[END_REF] and H (298 K) = 20 M atm -1 (3-pentanone) [START_REF] Janini | Determination of activity coefficients of oxygenated hydrocarbons by liquid-liquid chromatography[END_REF]. On the other hand, the Henry's law constants for carbonates are similar to those of the corresponding esters (RC(O)OR): H (298 K) = 8.7 M atm -1 (methyl acetate) [START_REF] Buttery | Volatilities of aldehydes, ketones, and esters in dilute water solutions[END_REF] and H (298 K) = 4.6 M atm -1 (ethyl propionate) [START_REF] Hine | The intrinsic hydrophilic character of organics compounds[END_REF].

Atmospheric implications

The atmospheric implications of this work can be obtained from the comparison of the lifetimes () of these organic carbonates in the troposphere with respect to their gas-phase removal by OH radicals and removal by liquid water in clouds.

In the gas-phase, as mentioned previously, the photolysis [START_REF] Calvert | Photochemistry[END_REF] of these carbonates as well as their reactions with the NO3 radical (Langer et al., 1993) or ozone (Atkinson et al., 1984) as secondary product [START_REF] Bilde | Atmospheric Chemistry of Dimethyl Carbonate : Reaction with OH Radicals, UV Spectra of CH 3 OC(O)OCH 2 and CH 3 OC(O)OCH 2 O 2 Radicals, Reactions of CH 3 OC(O)OCH 2 O 2 with NO and NO 2 , and Fate of CH 3 OC(O)OCH 2 O Radicals[END_REF].

Concerning the removal process by the aqueous phase, we need to know if the mass transfer limits the efficiency of this process. For this, the time-scale of the occurring processes, i.e. diffusion in the gas phase and mass accommodation process, have to be calculated.

The diffusion limitation is calculated from:

2 1 g D 8 drop d > c < γ 1 diff - = (XIII)
where ddrop is the diameter of droplets (1-50 m) contained in tropospheric clouds [START_REF] Kolb | Laboratory Studies of Atmospheric Heterogeneous Chemistry[END_REF] and Dg is the diffusion coefficient of carbonate in air, calculated from equation VII.

The corresponding gas diffusion time-scale diff can be estimated from the values of diff:

γ A c 4 1 1 τ diff c diff   = (XIV)
where Ac is the condensed phase surface to gas volume ratio (cm 2 /cm 3 ), taken as 5.010 -4 for the tropospheric clouds [START_REF] Kolb | Laboratory Studies of Atmospheric Heterogeneous Chemistry[END_REF]. Using this equation, the diffusion time-scale diff of both carbonates at 298 K for ddrop = 50 m are : 53 s (dimethyl carbonate) and 65 s (diethyl carbonate).

Mass accommodation can also limit the rate of gas uptake. The accommodation timescale accom can be estimated from the mass accommodation coefficient  as:

α A c 4 1 1 τ c accom   = (XV)
The values of  decrease from 0.14 to 0.01 between 265 and 279 K for both carbonates.

Taking a minimum value of  of 110 -2 at 279 K, the calculated accommodation time scale is 31 s and 35 s for dimethyl and diethyl carbonate, respectively. In regard to the tropospheric lifetimes of both carbonates in gas phase, the gas diffusion and mass accommodation are really fast process. Therefore, the uptake of these compounds by atmospheric droplets will not be limited by gas diffusion or mass accommodation.

One can then assume that organic carbonates in the gas phase will quickly reach their thermodynamic equilibrium with organic carbonates in the liquid phase. Under these conditions, the fraction XA,aq of a non reactive compound, A, dissolved in typical cloudwater droplets, is given by [START_REF] Seinfeld | Atmospheric Chemistry and Physics[END_REF]:

A, aq X A H RT L 1 A H RT L wc wc = + (XVI)
In this equation, the following units should be used: HA, the Henry Law coefficient in mol L -1 atm -1 ; the ideal gas constant, R = 0.08205 L mol -1 K -1 ; and the dimensionless liquid water content of the cloud, Lwc = 4.210 -7 . Lwc is related to the condensed phase surface to gas volume ratio (cm 2 /cm 3 ), Ac, by the following equation [START_REF] Kolb | Laboratory Studies of Atmospheric Heterogeneous Chemistry[END_REF]:

drop wc c d L 6 A = (XVII)
By using equation (XVII) and assuming that organic carbonates do not react in the aqueous phase, the fraction of dimethyl and diethyl carbonate in the atmospheric aqueous phase is about 510 -5 and 610 -5 , respectively at 298 K.

The small fractions of dissolved carbonates calculated above implies that wet deposition is not an efficient process for the removal of organic carbonates from the atmosphere. It is possible to estimate the removal rate of organic carbonates by assuming a first-order loss mechanism. In absence of reaction and assuming a fast equilibrium between gas and liquid atmospheric phase, the first-order removal constant by wet deposition, kwd, is given by (Brimblecombe et al., 1985):

wd k r R E exp(-z / Z ) Z 1 H RT L X X A wc = F H G I K J + R S T U V W (XVIII)
where Rr is the assumed annual rainfall rate (1 m/year), E is an enhancement factor due to droplet evaporation (assumed to be 1.33), z is a characteristic height for clouds (assumed to be 3.5 km), ZX is the scale height for the species (assumed to be 2.2 km (Brimblecombe et al., 1985)). The annual rainfall varies considerably from one environment to another, but the assumptions made here enable to estimate the time scale of this removal process. Based on these assumptions, the wet deposition lifetime is about 55 years for both carbonates. This is not a realistic lifetime, however, it shows that this process is unsignificant.

In the above calculation, it has been supposed that the organic carbonates did not react in the aqueous phase. In fact, they can be very slowly hydrolysed to form alcohols (methanol or ethanol in our case) and CO2 [START_REF] Crandall | Process for the Hydrolysis of Dialkyl Carbonates[END_REF]. The amount of organic carbonates able to be dissolved will be then slightly greater and the wet deposition lifetime will be a little smaller than the above value. But the wet deposition will remain negligible.

These carbonates can also react in the atmospheric aqueous phase with radicals such as OH, NO3, SO4 -. In this case, atmospheric lifetime due to reactive heterogeneous loss is expressed as [START_REF] Kolb | Laboratory Studies of Atmospheric Heterogeneous Chemistry[END_REF]:

( )

1/2 D 1/2 1/2 C WC τ k k HRT f L 1 τ + = (XIX)
where the term fc is the frequency of occurrence of the heterogeneous phase (fC = 0.15 in the troposphere), k is the reaction rate of the dissolved gas in the condensed phase (k = kOH where Dl is the condensed phase diffusion coefficient.

Rate constants of carbonates reaction with those radicals were measured by [START_REF] Parraudin | A steady-state flowtube approach for studying aqueous phase OH kinetics[END_REF]. At room temperature, the rate constants are (in units of M -1 s -1 ): k(DMC+OH) =

(5.1 ± 2.2)10 7 , k(DMC+SO4 -) = 1.310 5 , k(DMC+NO3) = 1.510 4 , k(DEC+OH) = (7.9 ± 3.2)10 8 , k(DEC+SO4 -) = 5.410 6 , k(DEC+NO3) = 8.410 4 . Assuming average concentrations of [OH]aq=510 -13 M, [SO4 -]aq=510 -13 M and [NO3]aq=110 -12 M in atmospheric aqueous phase [START_REF] Ervens | An extended and condensed tropospheric aqueous phase mechanism and its application[END_REF], tropospheric lifetimes are 175 and 8.9 years respectively for dimethyl and diethyl carbonates. We can then conclude aqueous phase reactions are negligible for both carbonates.

  are slow processes. The rate coefficient data obtained in the present study can then be used to estimate the tropospheric lifetimes of dimethyl and diethyl carbonate with respect to reaction with OH radicals (OH = 1/kOH[OH]). Assuming as usual an average OH concentration of 110 6 molecule cm -3 , tropospheric lifetimes of 33 days and 5 days in the gas-phase are calculated for dimethyl carbonate and diethyl carbonate respectively. The atmospheric oxidation of dimethyl carbonate initiated by OH radicals leads mainly to the formation of CH3OC(O)OC(O)H as primary product and HC(O)OC(O)OC(O)H

  [OH] + kNO3 [NO3] + kSO4-[SO4 -]) and D is the time required for diffusive mixing within the condensed phase defined by:

Figure Captions Figure 1 :

 Captions1 Figure Captions

Figure 2 :

 2 Figure 2: Plots of k 1 and k 2 vs. 1/T for the reaction of OH radicals with dimethyl and diethyl carbonate. The solid lines represent the Arrhenius parameter least-squares fits to the individual data points for each organic carbonate and the dashed line corresponds to the plot of k1=5.910 -12 exp(-1070/T) + 1.310 -14 exp(795/T). The error bars of the individual points are 2 and do not include estimated systematic errors.

Figure 3 :

 3 Figure3: Typical plots of ln(n/n-n) versus <c>S/4Fg for dimethyl carbonate (at 277.2K) on pure water. According to equation (IV), the slopes of such plots are a measure of the uptake coefficient  which were determined with the first straight data. The quoted errors for  include then a large estimated error of 10 % and 2 from the least-squares analysis.

Figure 4 :

 4 Figure4: Plot of the inverse of uptake coefficients 1/ as a function of the gas / liquid contact time for dimethyl carbonate (at 277.2K) on pure water showing that  was a function of time within our experimental conditions. According to the equation (V), the Henry's law constants were derived from the slope. The intercept is the inverse of the mass accommodation coefficient. The error bars are given at the 2 level.

Figure 5 :

 5 Figure5: Plot of the uptake coefficients  as a function of temperature on water and 0.1 M NaOH solution for dimethyl carbonate (figure5a) and diethyl carbonate (figure5b). The error bars are given at the 2 level.

Figure 6 :

 6 Figure6: Plot of the Henry's law constant H (M atm -1 ) versus the temperature for dimethyl carbonate (figure6a) and diethyl carbonate (figure6b). The error bars are given at the 2 level.

Figure 7 :

 7 Figure 7: Plot of H versus S. The error bars are given at the 1 level.

Figure 8 :

 8 Figure8: Plot of the mass accommodation  versus the temperature for dimethyl carbonate (figure8a) and diethyl carbonate (figure8b). The error bars are given at the 2 level.

Therefore, this work shows that gas phase reaction is the major atmospheric loss process for dimethyl and diethyl carbonates and that these compounds will not be found, or will exist in very small amount, in wet precipitations.

Acknowledgment

Support of this work by the French Ministry of Environment (PRIMEQUAL program), by the CNRS (PNCA program) and by the Region Alsace is gratefully acknowledged.


Maud Guglielmino

Alaa Allouch

Christophe A Serra

Stéphane Le Calvé
email: slecalve@unistra.fr.

DEVELOPMENT OF MICROFLUIDIC ANALYTICAL METHOD FOR ON-LINE GASEOUS FORMALDEHYDE DETECTION

Keywords: formaldehyde, microfluidics, annular flow, micro-device, indoor air

Novel analytical micro-device for quantification of gaseous formaldehyde • Gaseous Formaldehyde uptake through the establishment of a microfluidic annular flow • Formaldehyde detection using colorimetric cell using a liquid-core-waveguide

Introduction

Formaldehyde is a major pollutant of indoor air due to its multiple sources (materials, combustion, painting, etc.) [START_REF] Salthammer | Marutzky -Formaldehyde in the Indoor Environment[END_REF]. Several studies [START_REF] Wang | Characteristics of carbonyls: Concentrations and source strengths for indoor and outdoor residential microenvironments in China[END_REF][START_REF] Gilbert | Gauvin -Air change rate and concentration of formaldehyde in residential indoor air[END_REF][START_REF] Wang | Wang -Ambient formaldehyde and its contributing factor to ozone and OH radicals in a rural area[END_REF] have shown that indoor Formaldehyde concentrations are 2 to 15 times higher than those measured outdoor and may vary typically between 10 to 100 μg m -3 . [START_REF] Casset | Low exposo miteure to inhaled formaldehyde: effect on allergen bronchial response in asthmatics sensitized to mite[END_REF] [START_REF] Casset | Low exposo miteure to inhaled formaldehyde: effect on allergen bronchial response in asthmatics sensitized to mite[END_REF] have shown that Formaldehyde is implicated in allergic diseases, particularly for asthmatic people. As of 2004 Formaldehyde is considered as a carcinogenic compound for humans by the International Agency for Research on Cancer (IARC) [START_REF]IARC -Overall evaluation of carcinogenicity to humans, formaldehyde[END_REF]. French recommendations aim at limiting Formaldehyde concentrations in public buildings to 30 μg m -3 by 2015 and to only 10 μg m - 3 by 2023. Therefore, sensitive methods and potentially transportable instruments performing Formaldehyde measurements are highly required.

The conventional method to measure airborne Formaldehyde concentration [START_REF] Zhou | Mopper -Apparent partition coefficients of 15 carbonyl compounds between air and seawater and between air and freshwater; Implications for air-sea exchange[END_REF][START_REF] Müller | Determination of aldehydes and ketones in the atmosphere : A comparative long time study at an urban and a rural site in Eastern germany[END_REF][START_REF] Cerón | Diurnal and seasonal trends in carbonyl levels in a semi-urban coastal site in the Gulf of Campeche, Mexico[END_REF][START_REF] Wangchuk | Seasonal variations of outdoor air pollution and factors driving them in the school environment in rural Bhutan[END_REF] uses a DNPHcartridge sample followed by an off-line laboratory HPLC/UV analysis which is time-consuming and involves a laboratory treatment. In addition, such technique gives average concentrations over intervals of a few tens of minutes to one week, for active and passive samplings, respectively.

Many alternative methods oriented towards real-time and in-field detection, have been developed such as Hantzsch monitor, PTR-MS, infrared diode laser spectroscopy [START_REF]Salthammer -Photophysical properties of 3,5-diacetyl-1,4_dihydrolutidine in solution: application to the analysis of formaldehyde[END_REF][START_REF] Jobson | Coskey -Sample drying to improve HCHO measurements by PTR-MS instruments: laboratory and field measurements[END_REF][START_REF] Vlasenko | Abbatt -Formaldehyde measurements by Proton transfer reaction -Mass Spectrometry (PTR-MS): correction for humidity effects[END_REF][START_REF] Hanoune | Calvé -Formaldehyde measurements in libraries: Comparison between infrared diode laser spectroscopy and a DNPH-derivatization method[END_REF]. However, most of these methods rely on bulky apparatus and then are not adapted for indoor air monitoring where portability is a key point. Among the developed methods, some of them used reagents which react with Formaldehyde to produce color change which is conveniently used for the detection. Miniature and portable systems have been developed [START_REF] Toda | Gushiken -Mobile monitoring along a street canyon and stationary forest air monitoring of formaldehyde by means of a micro-gas analysis system[END_REF][START_REF] Allouch | Calvé -Transportable, fast and high sensitive near real-time analyzers: formaldehyde detection[END_REF]. Nevertheless, autonomic, and continuous monitoring over several weeks was often not possible since the reaction on the solid detection element was not reversible. In addition, the resolution of such sensors was usually not as good as needed to detect the very low Formaldehyde concentrations recommended by the state legislature.

As argued by Salthammer et al. in a review on Formaldehyde published in 2010 [START_REF] Salthammer | Marutzky -Formaldehyde in the Indoor Environment[END_REF], the method with derivatization to 3,5-Diacetyl-1,4-dihydrolutidine (DDL) in aqueous solution followed by fluorimetric determination is probably the most reliable method of measuring Formaldehyde in indoor air. A similar analytical technique, based on the uptake and concentration of Formaldehyde into an aqueous solution, followed by its specific and complete reaction with acetylacetone in presence of ammonium acetate to form DDL and then the quantification of DDL by fluorescence, has also been developed in our laboratory [START_REF] Le Calvé | Device and method for determining the concentration of a compound in an aqueous or gaseous phase[END_REF]. Such analyser is very sensitive (LOD < 1 µg m -3 ) and is considered to be portable and real-time due to its low weight (8 kg), its response time and temporal resolution (10 minutes). However, its major drawback is the high liquid reagent consumption since it operates at a liquid flow rate of 1.1 mL min -1 , which is a real limitation since the autonomy is then estimated to be only 15.2 hours with 1L of acetylacetone solution. In addition, more miniaturization is always needed for in-field monitoring.

This work aims at developing a new Formaldehyde analytical method which preserves precision, selectivity, sensitivity, and fast analysis in a single miniaturized instrument which will be suitable for field measurement with reagent autonomy sufficient for a one-month monitoring. The contribution of microfluidics in analytical system can allow advantageously achieving all these goals.

Materials and method

Chemicals

The reaction between Fluoral-P (or acetylacetone solution) and Formaldehyde producing DDL via a Hantszch reaction illustrated in Figure 1 was first investigated in 1972 (see [START_REF] Eisner | Kuthan -Chemistry of dihydropyridines[END_REF] for more details). Acetylacetone solutions (0.02M or 0.01M) were prepared by mixing 0.3 mL of acetic acid (100%, Merck), 0.2 mL of acetylacetone (99%, Merck), 15.4 g of ammonium acetate (98%, Sigma-Aldrich) in 100 or 200 mL Milli-Q water (18.2 MΩ.cm at 25°C, Millipore).

Gaseous Formaldehyde mixtures which concentration was varied from 19.5 to 81.6 µg m -3 (6.5x10 -7 to 2.7x10 -6 M respectively) were prepared by means of a homemade gaseous Formaldehyde source whose development and optimization was reported in a previous work [START_REF] Zheng | Développement d'un analyseur rapide et transportable du formaldéhyde dans l'air[END_REF]. Briefly, this source generates gaseous Formaldehyde by applying a controlled gas flow (5-20 mL min -1 ) in a microporous tube immersed in a concentrated Formaldehyde solution of 0.0925% regulated at 10°C by a Peltier module. This enriched gaseous Formaldehyde stream is then diluted with a controlled flow (500-2000 mL min -1 ) of pure air (> 99.999%) provided by Messer. The concentrated Formaldehyde solution of 0.0925% was prepared by mixing a commercial Formaldehyde solution (37% in water, Sigma-Aldrich) with Milli-Q water (18.2 MΩ.cm at 25°C, Millipore). Finally, the generated gaseous Formaldehyde concentrations were precisely quantified using the conventional sampling method on DNPH cartridges followed by HPLC/UV analysis already described elsewhere [START_REF] Marchand | Mirabel -Aldehyde Measurements in indoor environment in Strasbourg (France)[END_REF].

Formaldehyde solutions (5.3 or 53 g L -1 ) were prepared by mixing a commercial Formaldehyde solution (37% in water, Sigma-Aldrich) with Milli-Q water (18.2 MΩ.cm at 25°C, Millipore) to lower its concentration down to 1.8×10 -7 or 1.8×10 -6 M respectively.

Setups and experimental conditions 2.2.1 Overall setup for detection of gaseous formaldehyde

The setup used for the quantification of gaseous Formaldehyde is represented in Figure 2. It consisted in four sequential steps: 1) fluid feeding lines, 2) gaseous Formaldehyde uptake into the aqueous solution using an annular gas/liquid flow at room temperature (23°C), 3) derivatization reaction with acetylacetone at 65°C producing 3,5-Diacetyl-1,4-dihydrolutidine according to Figure 1 and finally 4) DDL detection by colorimetry. The aqueous solution of acetylacetone (0.01 M) was pumped at a flowrate of 35 µL min -1 thanks to a peristaltic pump (Ismatec, Reglo Lab) while a gas pump (NMP 850 KTDC, KNF) and a gas flow controller (low P flow, 0-100 mL.min -1 , Bronkhorst) ensured the constant flow rate (35 mL min -1 ) of either gaseous Formaldehyde mixture or pure air. The uptake arrangement was composed of a 1/16" peek T-junction (P-728-01, Upchurch) paired with two hydrophilic fused co-axial silica capillaries (Polymicro). The gas mixture flowed through the inner capillary (100 µm ID x 150 µm OD) while the gas/liquid flow exited the T-junction through a 530 µm ID x 680 µm OD outer capillary. The gas flow rate was thus 3 decades higher that the liquid flow rate which under a specific flow rates ratio gave rise (cf. §3.1) to the formation of an annular flow as illustrated in Figure 2. Due to a very high Henry's constant, 5000 ± 1200 M atm -1 [START_REF] Allou | Calvé -Henry's Law Constant measurements for formaldehyde and benzaldehyde as a function of temperature and water composition[END_REF], and a large interface area between gas and liquid phases promoted by the annular flow, the Formaldehyde was transferred from the gas to the liquid phase. The uptake of gaseous Formaldehyde was operated at room temperature (23°C) although the derivative reaction occurred at 65°C to increase the kinetic in order to obtain a full conversion of Formaldehyde to DDL. The gas was removed in flow by means of a microporous tube (µPT) and the resulting gas-free liquid phase containing the Formaldehyde entered a temperature-controlled oven (Croco-cil, Cluzeau Info Labo) where the derivatization reaction with the acetylacetone was promoted at 65°C. For the given liquid flow rate of 35 µL min -1 , the reaction's time of about 3.5 min was controlled through the length of the tubing installed inside the oven. After leaving the oven, the aqueous solution containing the derivatization reaction product (DDL) passed through another microporous tube to remove any bubble that may have been formed during the derivatization procedure including heating process. Finally, the gas-free solution entered the colorimetric cell for DDL detection. This cell was composed of 4 different parts (see Figure 2): i) a liquid-core-waveguide (LCW, BioGeneral), 207 µm ID and 44 cm length, with an inner coating of Teflon® AF 2400 allowing the light to travel through the liquid solution by total reflection. The LCW was wrapped in an aluminum foil to avoid any external parasite light; ii) 2 homemade one-inlet/twooutlet connectors with low dead volume and made of black polymeric material to avoid any parasite light; one port of both T-connector was used to connect the LCW, another port was used for the inlet and outlet (waste) of the DDL solution, finally the last port was used for a SMA adapter to connect in a straight manner the 1500 µm optical fibers (IDIL Fibres Optiques) of iii) a Deuterium-halogen light source (DH-2000, Ocean Optics) and iv) a minispectrometer (C10082CAH, Hamamatsu).

Setup for gas/liquid phase diagram determination

To determine the flow pattern of the gas/liquid flow inside the outer capillary at room temperature, the setup represented in Figure 3 was used. A syringe pump (Phd 2000, Harvard Apparatus) was used to pump a fresh acetylacetone solution (0.01 M) through a PTFE tubing (300 µm ID x 25 cm). Another syringe pump was used to inject air through a fused silica capillary (810 µm ID x 110 cm). Then the two fluids entered the same aforementioned uptake arrangement detailed in Figure 3. 10 cm downstream to the T-junction, an optical microscope (Eclipse TS 100, Nikon) was placed above the outer capillary to take pictures and record the flow pattern thanks to a CCD camera (PIKE F-032C, Allied Technology) and an imaging software (Hiris, R&D Vision). Depending on the flow rates of both liquid and gas phases, the flow pattern observed varied from annular flow to slug slow. Thus, to determine the flow pattern inside the outer capillary, the liquid flow rate was varied from 5 to 35 µL/min while the gas flow rate was varied from 5 to 35 mL/min. Upon modification of an operating parameter, at least 10 min were elapsed before to record the flow pattern such as the new steady state was reached.

Setup and experimental conditions to evaluate of the colorimetric detection using liquid Formaldehyde solutions

The calibration of the colorometric cell was performed with a modified version of the overall setup shown in Figure 4. The Formaldehyde gas line was replaced by a liquid line of an aqueous Formaldehyde solution (0.02 M) pumped thanks to a syringe pump (Phd 2000, Harvard apparatus). A simple peek T junction (P-728-01, Upchurch) ensured the mixing between the two liquid flows before entering in a 0.75 mm ID x 3.2 m capillary placed inside the same aforementioned temperaturecontrolled oven to promote the derivatization reaction.

Step 4, i.e., the colorimetric detection, remained the same. Upon dilution with the acetylacetone solution, the concentration of aqueous Formaldehyde was fixed to 5.3 μg L -1 (1.8×10 -7 M).

Setup and experimental conditions for the gaseous or aqueous Formaldehyde calibration

In order to evaluate the uptake yield, both gas and liquid calibrations were performed using the setup detailed in Figure 2. The length of the uptake cell was fixed to 200 cm whereas the internal diameter and the length of the colorimetric cell detection were 207 microns and 44 cm, respectively. The liquid and gas flow rates were set to 35 μL min -1 and 35 mL min -1 , respectively.

In fact, the experimental apparatus for carrying out liquid phase Formaldehyde calibration is similar to that used for the calibration concentrations of gaseous Formaldehyde. The only two differences are the following: 1) synthetic air free of Formaldehyde replaces the gaseous Formaldehyde mixtures to keep exactly the same residence time in the uptake cell and 2) acetylacetone solution 0.01 M is replaced by a mixture of acetylacetone doped with a known concentration of Formaldehyde prepared as detailed below. First, Formaldehyde concentrations ranging from 20.1 to 316.0 μg L -1 (6.7 x 10 -7 to 1.1 x 10 -5 M) were prepared in water. They were subsequently diluted by approximately half in a solution of acetylacetone 0.02 M to directly obtain Formaldehyde concentrations ranging from 9.4 to 153.8 μg L -1 (from 3.1 x 10 -7 to 5.1 x 10 -6 M) in a solution of acetylacetone 0.01M.

Results and discussion

Gas/Liquid phase diagram

To determine the combination of gas and liquid flow rates that provide an annular flow, the acetylacetone/air phase diagram was determined experimentally following the procedure described in section 2.2.2 and illustrated in Figure 3. Results are presented for the 530 µm ID outer capillary at room temperature (23°C) in Figure 5.A. Different patterns were observed, namely slug, slug-annular and annular (Figure 5.B). The slug pattern is to be found in the left part of the phase diagram, i.e., when the gas flow rate is low. When the gas flow rate is increased, an intermediate region appears, and the flow adopts a slug-annular pattern. Finally, when the gas to liquid flow rate ratio is greater than 1,000, a large annular region covers the whole right-hand part of the phase diagram.

In an attempt to compare our results with the literature, data of Figure 6.A were plotted as a function of the gas and liquid superficial velocities and put in regards with the air/water phase diagram obtained in [START_REF] Sur | Adiabatic air-water two-phase flow in circular microchannels[END_REF] with a 324 µm ID capillary at room temperature (Figure 6.B). It is observed that only a small region of our phase diagram (red rectangle) can be compared since most of our data were produced with smaller superficial liquid velocities; moreover, the size of the two capillaries was different. Nevertheless, the agreement is fairly good. Indeed, Sur and Liu [START_REF] Sur | Adiabatic air-water two-phase flow in circular microchannels[END_REF] diagram shows a transition between slug and slug-annular patterns when the superficial gas and liquid velocities reaches 1.5 m s -1 and 2×10 -3 ms -1 , the same for Figure 6.A. Finally, the annular flow is obtained in our case when the superficial gas velocity is higher than 2.5 m s -1 which is close to the value of 3 m s -1 reported by Sur and Liu in their phase diagram.

To ensure the quantitative transfer of the gaseous Formaldehyde into the liquid phase for further aqueous Formaldehyde derivatization and subsequent DDL quantification in the colorometric cell, the interface area between the gas and liquid phase should be maximized. From Figure 6.B, it can be observed that this is the case only in the annular flow for which the interface area per volume unit of gas/liquid mixture is directly proportional to the radius of the gas/liquid interface according to the following equation:

(

) 1
where AI is the interface area per unit of volume, RI and Rcap the radii of the interface and capillary (i.e., 265 µm) respectively.

From the analysis of our typical snapshots of the annular flow (Figure 5.B), the interface surface was roughly estimated to be equal to 1.6 m 2 m -3 .

Evaluation of the colorimetric detection using liquid Formaldehyde solutions

This experiment was conducted to demonstrate that the use of a liquid-core-waveguide as colorimetric detection cell well checked the Beer-Lambert law and thus the value of the molar extinction coefficient obtained corresponded to that of a molecule of DDL. Four LCW lengths were tested, 10, 20, 40 and 90 cm for three liquid-core-waveguides of different internal diameters, 207, 400 and 1000 µm. The concentration of aqueous Formaldehyde was fixed to 5.3 μg L -1 (1.8×10 -7 M) in order to determine as accurately as possible, the detection limits used as evaluation parameters in these experiments.

Liquid flow rate was fixed to 104 μL min -1 which represents a ten-fold reduction compared to the flow rate used in our previous analytical method [START_REF] Le Calvé | Device and method for determining the concentration of a compound in an aqueous or gaseous phase[END_REF]. The corresponding LCW residence times varied from 0.03 minutes for a waveguide of 207 µm ID and 10 cm long to 6.79 minutes for a waveguide of 1000 µm ID and 90 cm long.

According to the Beer-Lambert, absorbance increases linearly with the length of the waveguide whatever its ID as illustrated in Figure 7. From the obtained slope, the molar extinction coefficient of DDL () can be extracted. This value is equal to ε = 7320 ± 610 M -1 cm -1 at 415 nm, the error bars correspond to 2. This result is in very good agreement with the value reported in the literature for DDL, ε = 7500 M -1 cm -1 [START_REF]Salthammer -Photophysical properties of 3,5-diacetyl-1,4_dihydrolutidine in solution: application to the analysis of formaldehyde[END_REF].

The detection limits determined for both colorimetric cells (i.e., LCW ID of 207 and 1000 microns) are summarized in Table 1 for the different lengths of the waveguide and vary between 0.3 and 1.9 μg L -1 using a signal noise ratio of 3. Even if the detection limit is slightly lower with the LCW of 1000 µm ID, the following experiments were conducted with the LCW of 207 µm because of the solution residence time which is significantly shorter, the LCW length being fixed to 44 cm.

Gaseous Formaldehyde calibration

Regarding the above results obtained on the Gas/Liquid phase diagram and the colorimetric detection using LCW, the microfluidic analytical method shown in Figure 2 was calibrated using 1) a liquid and gas flow rates of 35 µL min -1 and 35 mL min -1 respectively and a LCW of 207 µm ID and 44 cm length in order to obtain 1) an annular flow and 2) to reduce significantly the time response.

The calibration was performed for gaseous Formaldehyde concentrations varying from 19.5 to 81.6 μg m -3 (6.5×10 -7 to 2.7×10 -6 M), this range corresponds to Formaldehyde concentrations typically found in indoor air. The absorbance signals obtained for these concentrations are shown in Figure 8. They are centered on a wavelength of 415 nm corresponding to the maximum absorbance of the DDL in accordance with the literature [START_REF]Salthammer -Photophysical properties of 3,5-diacetyl-1,4_dihydrolutidine in solution: application to the analysis of formaldehyde[END_REF][START_REF]Nash -The colorimetric estimation of formaldehyde by means of the Hantzsch reaction[END_REF]. The signals obtained for high concentrations are much noisy at the optimum absorption wavelength, this is partly due to the high absorbance values, close to 1.

As shown in Figure 9, the absorbance signal increases linearly (R² = 0.999) when the gas phase concentration increases. Considering an absorbance noise of 2.7×10 -3 , the detection limit of the analytical device in this configuration (gas uptake and colorimetric detection) is in the order of 0.7 μg m -3 for a signal noise ratio equal to 3. The limit quantification was estimated to 2.3 μg m -3 for a signal to noise ratio equal to 10.

Uptake yield

Ideally, the uptake efficiency of gaseous Formaldehyde must be reproducible and equal to 100%, particularly if the Beer-Lambert law is used to calculate the concentration of Formaldehyde in the solution and therefore to deduce the concentration of gaseous formaldehyde.

For a DDL molecule, the molar absorption coefficient  is equal to 7500 M -1 cm -1 from the literature [START_REF]Salthammer -Photophysical properties of 3,5-diacetyl-1,4_dihydrolutidine in solution: application to the analysis of formaldehyde[END_REF]. This value agrees well with our experimental value of 7320 ± 610 M -1 cm -1 (see section 3.2) obtained with our absorption cell composed of a liquid-core-waveguide. Knowing the absorbance measured experimentally, the molar extinction coefficient and the optical path length (equivalent to the length of the waveguide), it is possible to determine the experimental concentration of the DDL by applying the Beer-Lambert law:

(

) 2
where A is the absorbance,  the molar absorption coefficient, l the optical path length and c the compound concentration.

The number of Formaldehyde moles experimentally trapped (nHCHO exp) into the solution can be calculated from the measured absorbance. If the uptake of the gaseous Formaldehyde is total, the number of gaseous Formaldehyde moles is quantitatively transferred into the aqueous solution, which allows to determine the number of Formaldehyde moles theoretically trapped (nHCHO th) into the solution. The uptake yield is then the ratio between the number of Formaldehyde moles trapped experimentally and the theoretical value considering an uptake yield of 100%.

(

) 3
In our series of experiments, the uptake yield for gaseous Formaldehyde concentrations varying from 19.5 to 81.6 μg m -3 (6.5×10 -7 to 2.7×10 -6 M) was 90 ± 2% whatever the concentrations as illustrated in Table 2. This uptake yield is then quite high and ensures almost the quantitative Formaldehyde transfer from gas to the aqueous solution.

Conclusions

The acetylacetone solution/Formaldehyde gas phase diagram was determined for a 530 µm ID capillary by varying the liquid and gas flow rate in the range 5 to 35 µL min -1 and 5 to 35 mL min -1 respectively. The annular flow, the sole flow pattern among the three we observed which maximizes the surface area between gas and liquid required for a quantitative transfer of gaseous Formaldehyde into the liquid phase, was found to occupy a large region of the phase diagram for liquid flow rate above 5 min -1 and gas to liquid flow rate ratios greater than 1000.

Our experimental work performed under controlled gaseous Formaldehyde concentrations showed that the device based on a microfluidic annular two-phase flow to achieve the uptake of gaseous Formaldehyde had a linear response permitting to quantify typical indoor air concentrations of Formaldehyde in the range 0-100 µg m -3 . This new device is characterized by its excellent analytical performances such as the observed high uptake yield of 90% as well as the relatively low detection and quantification limits, i.e., 0.7 and 2.3 μg m -3 respectively.

With 1L of acetylacetone solution and a liquid flow rate of 35 µL min -1 , the reagent autonomy increases significantly up to 19.8 days for a continuous Formaldehyde monitoring against only 15.2 hours for the previous analytical technique.

Acknowledgement

This work is supported by ADEME and Region Alsace, REALISE, the program PRIMEQUAL and ANR (ANR-11-ECOT-0013).