Coraline Mattei

Henri Wortham

Etienne Quivet
email: etienne.quivet@univ-amu.fr

Heterogeneous atmospheric degradation of pesticides by ozone: influence of relative humidity and particle type

Keywords: pesticides, heterogeneous reactivity, ozonolysis, kinetics, silica particles, relative humidity

In the atmosphere pesticides can be adsorbed on the surface of particles, depending on their physico-chemical properties. They can react with atmospheric oxidants such as ozone but parameters influencing the degradation kinetics are not clear enough. In this study the heterogeneous ozonolysis of eight commonly used pesticides (i.e., difenoconazole, tetraconazole, cyprodinil, fipronil, oxadiazon, pendimethalin, deltamethrin, and permethrin) adsorbed on hydrophobic and hydrophilic silicas, and Arizona dust at relative humidity ranging from 0% to 80% was investigated. Under experimental conditions, only cyprodinil, deltamethrin, permethrin and pendimethalin were degraded by ozone. Secondorder kinetic constants calculated for the pesticides degraded by ozone ranged from (4.7 ± 0.4) × 10 -20 cm 3 molecule -1 s -1 (pendimethalin, hydrophobic silica, 55% RH) to (2.3 ± 0.4) × 10 -17 cm 3 molecule -1 s -1 (cyprodinil, Arizona dust, 0% RH). Results obtained can contribute to a better understanding of the atmospheric fate of pesticides in the particulate phase and show the importance of taking humidity and particle type into account for the determination of pesticides atmospheric half-lives.

Introduction

Pesticides are used worldwide to control pests in agricultural production (e.g., vineyards, orchards, and farming) and in many nonagricultural settings (e.g., home, public spaces, gardens and parks, and industrial areas). The important increase in their utilization and their potentially adverse human health effects make their environmental fate to be a hot topic.

Atmospheric pesticide contamination was observed in urban and rural areas with concentration levels from some picogram per cubic meter (pg m -3 ) to several nanogram per cubic meter (µg m -3 ) [START_REF] Coscollà | Particle size distributions of currently used pesticides in a rural atmosphere of France[END_REF][START_REF] Coscollà | Particle size distributions of currently used pesticides in ambient air of an agricultural Mediterranean area[END_REF][START_REF] Estellano | Assessing Levels and Seasonal Variations of Current-Use Pesticides (CUPs) in the Tuscan Atmosphere, Italy, Using Polyurethane Foam Disks (PUF) Passive Air Samplers[END_REF][START_REF] Zivan | Airborne organophosphate pesticides drift in Mediterranean climate: The importance of secondary drift[END_REF][START_REF] Zivan | Primary and secondary pesticide drift profiles from a peach orchard[END_REF]. This contamination can be due to spray drift during pesticide applications (about 15 to 40%; [START_REF] Sinfort | Influence des conditions et matériels de pulvérisation sur les pertes de pesticides au sol et dans l'air en viticulture Languedocienne[END_REF][START_REF] Yates | Emissions of 1,3-Dichloropropene and Chloropicrin after Soil Fumigation under Field Conditions[END_REF][START_REF] Zivan | Airborne organophosphate pesticides drift in Mediterranean climate: The importance of secondary drift[END_REF][START_REF] Zivan | Primary and secondary pesticide drift profiles from a peach orchard[END_REF], post-application volatilization from treated plants [START_REF] Zivan | Airborne organophosphate pesticides drift in Mediterranean climate: The importance of secondary drift[END_REF][START_REF] Zivan | Primary and secondary pesticide drift profiles from a peach orchard[END_REF], soil [START_REF] White | Ambient Air Concentrations of Pesticides Used in Potato Cultivation in Prince Edward Island, Canada[END_REF] or aquatic surfaces [START_REF] Luo | Modeling complexity in simulating pesticide fate in a rice paddy[END_REF]) (about 0.1 to several dozen %; [START_REF] Lichiheb | Measuring Leaf Penetration and Volatilization of Chlorothalonil and Epoxiconazole Applied on Wheat Leaves in a Laboratory-Scale Experiment[END_REF], and wind erosion [START_REF] Glotfelty | Volatilization and wind erosion of soil surface applied atrazine, simazine, alachlor and toxaphene[END_REF].

Once in the atmosphere, pesticides partition among the gas, particulate, and liquid phases depending on their physicochemical properties and the environmental conditions [START_REF] Sanusi | Gas-particle Partitioning of Pesticides in Atmospheric Samples[END_REF][START_REF] Scheyer | Analysis of Some Organochlorine Pesticides in an Urban Atmosphere (Strasbourg, East of France)[END_REF][START_REF] Yao | Pesticides in the Atmosphere Across Canadian Agricultural Regions[END_REF][START_REF] Vogel | Pesticides in Rain in Four Agricultural Watersheds in the United States[END_REF]. Of importance, [START_REF] Sauret | Study of the Effects of Environmental Parameters on the Gas/Particle Partitioning of Current-Use Pesticides in Urban Air[END_REF] outlined that pesticides recently placed on the market are less volatile than the older ones (e.g., organochlorine compounds) and are mainly associated to the atmospheric particulate phase. Atmospheric sinks of pesticides include wet or dry deposition [START_REF] Majewski | Pesticides in Mississippi air and rain: A comparison between 1995 and 2007[END_REF], and direct [START_REF] Borras | Atmospheric degradation of the organothiophosphate insecticide -Pirimiphos-methyl[END_REF] or indirect [START_REF] Socorro | Heterogeneous OH Oxidation, Shielding Effects, and Implications for the Atmospheric Fate of Terbuthylazine and Other Pesticides[END_REF] photochemical degradation.

The indirect photochemical lifetime of pesticides in the particulate phase (i.e., adsorbed on atmospheric particles) is mostly governed by their chemical reactivity toward hydroxyl and nitrate radicals, and ozone as photolytic intermediate by-products.

The atmosphere contains particles with concentrations from few thousands to several hundreds of thousands of particles per cubic centimeter. Most pesticides are mainly accumulated in the ultrafine-fine (below 1 µm) size fractions [START_REF] Coscollà | Particle size distributions of currently used pesticides in a rural atmosphere of France[END_REF][START_REF] Coscollà | Particle size distributions of currently used pesticides in ambient air of an agricultural Mediterranean area[END_REF]. Particles are also exposed to water vapor in atmosphere (at a typical relative humidity (RH) range from 30% to 100% at ambient temperature) that produces mono or multilayer water film on their surfaces depending on the RH [START_REF] Keskinen | On-Line Characterization of Morphology and Water Adsorption on Fumed Silica Nanoparticles[END_REF]. These water layers can have important consequences for heterogeneous reactivity in the atmosphere as the kinetics of many reactions is strongly dependent on the phase of aerosol particles [START_REF] Knipping | Experiments and Simulations of Ion-Enhanced Interfacial Chemistry on Aqueous NaCl Aerosols[END_REF]. Atmospheric particles are diverse in origin, size, and chemical composition [START_REF] Seinfeld | Atmospheric Chemistry and Physics: From Air Pollution to Climate Change[END_REF].

They originate from natural sources such as desert dust, volcanic ashes, and marine aerosols, or from anthropogenic sources as vehicular traffic, biomass burning, and fossil fuel combustion [START_REF] Salameh | PM 2.5 chemical composition in five European Mediterranean cities: a 1-year study[END_REF].

Several kinetic studies of heterogeneous ozonolysis of pesticides (Table 1; [START_REF] Meng | Heterogenous ozonation of suspended malathion and chlorpyrifos particles[END_REF][START_REF] El Masri | A mechanistic and kinetic study of the heterogeneous degradation of chlorpyrifos and chlorpyrifos oxon under the influence of atmospheric oxidants: ozone and OH-radicals[END_REF][START_REF] Bouya | Kinetics of the Heterogeneous Photo Oxidation of the Pesticide Bupirimate by OH-Radicals and Ozone under Atmospheric Conditions[END_REF]Socorro et al., 2015 and reference therein) were carried out under different experimental conditions as ozone mixing ratio (e.g., from 0.4 to 86 ppm), RH (e.g., from 0% to 80% RH and uncontrolled), temperature (e.g., from 19°C to 26°C), and type of particles (e.g., hydrophilic and hydrophobic silicas, quartz surfaces, ZnSe crystals, and azelaic acid aerosols). As a result, literature data is often difficult to compare.

The aim of the present work is to better understand the influence of humidity and particle type on the heterogeneous degradation of pesticides by ozone. The experimental protocol and the eight studied pesticides (i.e., difenoconazole, tetraconazole, cyprodinil, fipronil, oxadiazon, pendimethalin, deltamethrin, and permethrin) are identical as those used in previous studies [START_REF] Socorro | Heterogeneous Reactions of Ozone with Commonly Used Pesticides Adsorbed on Silica Particles[END_REF](Socorro et al., , 2016b)). Pesticides are representative of major applications, i.e., herbicides, insecticides, and fungicides, and were chosen for their worldwide utilization but also for their physico-chemical properties. The heterogeneous ozonolysis was carried out at 25°C with a range of relative humidity from 0% to 80% RH. Three kinds of silica particles (i.e., hydrophilic and hydrophobic silicas, and Arizona dust) were used because silica is regarded as one of the main constituents of atmospheric mineral dust and widely used as the model particles for heterogeneous reactions.

Experimental section

Chemicals

Cyprodinil (purity 99.8%), deltamethrin (99.7%), difenoconazole (97.0%), fipronil (97.5%), oxadiazon (99.9%), pendimethalin (98.8%), permethrin (98.3%), and tetraconazole (99.0%) were purchased from Sigma-Aldrich (PESTANAL®, analytical standard) and were used as received. The chemical structures of the pesticides under study are depicted in Fig. SI1 and their physico-chemical properties are given in Table SI1.

Particles

Three commercial silica particles were used to mimick atmospheric mineral aerosols: AEROSIL R812 (purchased from Degussa) thereafter called "hydrophobic silica", AEROSIL 255 (Evonik Industries) called "hydrophilic silica", and ISO 12103-1, A1 Ultrafine Test Dust (Powder Technology Inc.) called "Arizona dust". Composition: Hydrophobic and hydrophilic silicas (> 99.8 wt%), and Arizona dust (69-77 wt%) contains mainly SiO2. Arizona dust is also composed of other various mineral oxides (Al2O3 (8-14 wt%), Fe2O3 (4-7 wt%), Na2O (1-4 wt%), CaO (2.5-5.5 wt%), K2O (2-5 wt%), MgO (1-2 wt%), and TiO2 (0-1 wt%)) and can be thought of as a model dust that originates from deserts [START_REF] Welti | Influence of Particle Size on the Ice Nucleating Ability of Mineral Dusts[END_REF][START_REF] Coscollà | Particle size distributions of currently used pesticides in a rural atmosphere of France[END_REF][START_REF] Coscollà | Particle size distributions of currently used pesticides in ambient air of an agricultural Mediterranean area[END_REF]. Particle size: The mean primary particle size of hydrophobic and hydrophilic silica particles ranges from 5 nm to 50 nm [START_REF] Evonik | AEROSIL® -Fumed Silica[END_REF]. However, most of them can be arranged as agglomerates with an aggregate size roughly measured mainly around 5 µm, sometimes up to 25 μm (Fig. SI2-SI4). Arizona dust particles are distributed in all size classes and 95.5-97.5 vol% are less than 11 μm. These size ranges are consistent with field observations that show that pesticides are distributed in the fine (0.1-1 µm), ultrafine (0.03-0.1 µm), and coarse (1-10 µm) particle size fraction, and that no pesticides were detected in the size fraction >10 µm [START_REF] Xu | Size distribution and seasonal variations of particle-associated organochlorine pesticides in Jinan, China[END_REF][START_REF] Coscollà | Particle size distributions of currently used pesticides in a rural atmosphere of France[END_REF][START_REF] Coscollà | Particle size distributions of currently used pesticides in ambient air of an agricultural Mediterranean area[END_REF]. Specific surface area (SSA; BET method):

Hydrophobic and hydrophilic silica particles have a specific surface area of (260 ± 30) m 2 g -1 and (255 ± 25) m 2 g -1 , respectively [START_REF] Evonik | AEROSIL® -Fumed Silica[END_REF]. Arizona dust has a specific surface area of (20.6 ± 0.2) m 2 g -1 (measured). Surface chemistry and hygroscopicity: Surfaces of hydrophobic and hydrophilic silica particles are mainly covered by silanol and siloxane groups. Silanol groups have a hydrophilic nature (i.e., readily mix with water) whereas the siloxane groups are chemically inert and hydrophobic. [START_REF] Vlasenko | Generation of Submicron Arizona Test Dust Aerosol: Chemical and Hygroscopic Properties[END_REF] suggest that Arizona dust particles are essentially non-hygroscopic (i.e., hydrophobic) due to the low amount of soluble material.

Particles coating

Hydrophobic silica, hydrophilic silica, and Arizona dust particles were independently coated with pesticides according to a liquid/solid adsorption. In an amber Pyrex bulb of 500 cm 3 , 600 mg of particles were mixed with 6 mL of a pesticide solution (all 8 pesticides at a concentration of 20 mg L -1 in dichloromethane (for HPLC, ≥ 99.8%, Sigma-Aldrich)), i.e., the load of pesticides on silica particles was about 0.02% by weight) and 40 mL of dichloromethane. After a 5-min ultrasound treatment, dichloromethane was evaporated by a rotary evaporator (Rotavapor R-114, Büchi) at 40°C and 850 mbar. This process allows a reproducible coating of the pesticides on the particle's surface [START_REF] Socorro | Heterogeneous Reactions of Ozone with Commonly Used Pesticides Adsorbed on Silica Particles[END_REF]. Assuming a uniform particle surface coverage for the pesticide molecules and a spherical geometry for particles, the percentage of the particle surface coated with individual pesticide was between 0.3% and 0.5% of the monolayer for hydrophobic and hydrophilic silicas (See calculation in supplementary information). Then, the total coated particle surface was 2.8% and 2.9% for hydrophobic silica and hydrophilic silica, respectively, which is much less than a monolayer. Due to their weak SSA, the percentage of the Arizona dust particle surface coated with individual pesticide was between 3.4% and 5.7%, which corresponds to a larger total coated particle surface (35.9%).

Ozonolysis experiments

The experimental setup was previously described in detail in [START_REF] Socorro | Heterogeneous Reactions of Ozone with Commonly Used Pesticides Adsorbed on Silica Particles[END_REF] (Fig. SI5).

Briefly, a 500 cm 3 amber Pyrex bulb containing about 500 mg of dried particles coated with pesticides was fixed to a modified rotary evaporator and placed in a thermostated water bath (25 ± 1°C). Ozone was generated by passing a flow of purified air through an ozone generator.

Particles coated with pesticides were exposed to an air flux containing an ozone mixing ratio of 400 ppb (i.e., 9.85 • 10 12 molecules cm -3 ) continuously monitored with a photometric ozone analyzer. The relative humidity (RH) ranged from 0% to 80%. The required humidity was obtained by mixing at different rate of dry and wet gaseous fluxes of purified air. The resulting humidity was measured with a humidity probe with uncertainties of 2% and the sum of the three air fluxes in the reaction flask was 500 mL min -1 . Experiments were all conducted for a duration of 26 h.

Extraction and pesticides quantification

During ozone exposure, 30 mg aliquots of particles were regularly sampled in order to quantify the remaining adsorbed pesticides on their surface. Each 30 mg aliquot of particles was individually introduced in a 33 mL stainless steel cell with an internal standard solution (Triphenyl phosphate, 99.9%, Sigma-Aldrich) and pesticides were extracted by accelerated solvent extraction (ASE 350, Dionex) with dichloromethane. Afterwards, the extracts were concentrated under a nitrogen flow using a concentration workstation (TurboVap II, Biotage).

Analysis of the obtained solutions were realized using gas chromatography coupled to tandem mass spectrometry (GC/MS-MS), with a Trace GC Ultra (Thermo Scientific) coupled to a TSQ Quantum™ Triple Quadrupole (Thermo Scientific) using electron impact ionization (70 eV).

More details about ASE extraction, concentration, and GC/MS-MS analysis are available in [START_REF] Socorro | Heterogeneous Reactions of Ozone with Commonly Used Pesticides Adsorbed on Silica Particles[END_REF].

Determination of second-order rate constants and half-lives toward ozone

Considering that ozone was continuously drifting in the reactor and that it was used in excess, a pseudo-first order kinetic constant was assumed:

𝐿𝑛 ( [𝑃𝑒𝑠𝑡𝑖𝑐𝑖𝑑𝑒 (𝑎𝑑𝑠) ] 𝑡 [𝑃𝑒𝑠𝑡𝑖𝑐𝑖𝑑𝑒 (𝑎𝑑𝑠) ] 0 ) = -(𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼 + 𝑘 𝑑𝑒𝑠 (𝑝𝑎𝑟𝑡) 𝐼 + 𝑘 ℎ𝑦𝑑 (𝑝𝑎𝑟𝑡) 𝐼 ) × 𝑡 (1)
where 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼 (s -1 ) is the pseudo-first order rate constant of the reaction between ozone and the pesticides, 𝑘 𝑑𝑒𝑠 (𝑝𝑎𝑟𝑡) 𝐼 (s -1 ) is the first order desorption rate constant, 𝑘 ℎ𝑦𝑑 (𝑝𝑎𝑟𝑡) 𝐼 (s -1 ) is the pseudo-first order hydrolysis rate constant, t (s) is the time of ozone exposure, and

[Pesticide(ads)]t/[Pesticide(ads)]0 is the pesticide concentration normalized to the initial pesticide concentration.

The pseudo-first-order reaction rate constants for the heterogeneous ozonolysis of the particlephase pesticides were determined by analyzing their corresponding temporal profiles in time frame from 0 to 26 h, for 400 ppb ozone mixing ratio.

In order to determine the second-order rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡)

𝐼𝐼

, the experimental pseudo-first order reaction rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡)

𝐼

were plotted as a function of the ozone concentrations.

To simulate the kinetic mechanisms of the heterogeneous reactions the Langmuir-Rideal (L-R, known also as Eley-Rideal) and Langmuir-Hinshelwood (L-H) models are commonly used. In a previous work [START_REF] Socorro | Heterogeneous Reactions of Ozone with Commonly Used Pesticides Adsorbed on Silica Particles[END_REF], it was demonstrated that both L-R and L-H models show comparable reactivity for the same pesticide as the ones used in this study. Fig. 1 shows the pseudo-first order rate constant (𝑘 𝑂 3(𝑝𝑎𝑟𝑡)

𝐼

) determined in this work and reported by [START_REF] Socorro | Heterogeneous Reactions of Ozone with Commonly Used Pesticides Adsorbed on Silica Particles[END_REF] as a function of ozone concentrations for cyprodinil adsorbed on hydrophilic silica. The same good agreement between the two studies is observed for the eight pesticides under study. As a result, we assumed to calculate the second-order rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡)

𝐼𝐼

(cm 3 molecule -1 s -1 ) with only one ozone mixing ratio, i.e., 400 ppb, using a Langmuir-Rideal model.

The second-order rate constant was calculated as follows:

𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼 = 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 × [𝑂 3(𝑔𝑎𝑠) ] (2)
where [𝑂 3(𝑔𝑎𝑠) ] is the constant ozone mixing ratio of 400 ppb (i.e., 9.85 × 10 12 molecules cm - 3 ).

Half-lives corresponding to the heterogeneous atmospheric degradation of pesticides toward ozone were calculated for each specific experimental condition. Ozone mixing ratio used for calculation was 40 ppb [START_REF] Vingarzan | A review of surface ozone background levels and trends[END_REF], and half-lives (s) were obtained with the following equation:

t ½ O 3(part) = 𝑙𝑛2 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 × [𝑂 3(𝑔𝑎𝑠) ]
(3)

Results and discussion

Desorption and hydrolysis of pesticides adsorbed on particles

To estimate the loss of pesticide by desorption from particles and by hydrolysis, experiments were carried out for the three kinds of particles, with 500 mL min

𝐼

) at different humidity level are presented for each kind of particles in Fig. 2. They ranged from (2.0 ± 4.2) × 10 -7 s -1 to (3.4 ± 1.7) × 10 -6 s -1 , from (0.5 ± 2.2) × 10 -7 s -1 to (3.8 ± 0.3) × 10 -6 s -1 , and from (3.7 ± 0.7) × 10 -6 s -1 to (2.4 ± 0.4) × 10 -5 s -1 , for hydrophilic, hydrophobic, and Arizona dust particles, respectively. SI1) and their hydrolysis half-lives higher than 30 days (PPDB, 2017). As a result, pesticide losses observed in our experimental conditions are expected to be due to desorption rather than hydrolysis.

Fig. 3 shows that the RH does not significantly influence pesticides desorption when adsorbed on hydrophilic silica and Arizona dust while a slight influence is measured on hydrophobic particles. On the other hand, higher (𝑘 𝑑𝑒𝑠 (𝑝𝑎𝑟𝑡)

𝐼

+ 𝑘 ℎ𝑦𝑑 (𝑝𝑎𝑟𝑡)

𝐼

) are observed for Arizona dust than for hydrophilic silica particles.

These results are tricky to explain but due to their weak SSA, a larger fraction coated particle surface (35.9%) is expected for the Arizona dust which promotes the formation of pesticide clusters on particle surface. This possibly makes desorption easier and more important than for the other particles. The nature of the surface (greater proportion of metal oxides) could also play a key role. For hydrophobic silica, the RH dependence could be induced by the expected small amount of adsorbed water. Indeed, at high RH, a competition may take place between water and pesticide which would increase desorption. This hypothesis is contradicted by the results observed for hydrophilic particles, unless it is presumed that a larger amount of adsorbed water (as is the case even for low RH) makes it possible to keep the desorbed pesticides in the liquid phase.

All kinetic constants measured during ozonolysis experiments were corrected using rate constants of desorption and hydrolysis (𝑘 𝑑𝑒𝑠 (𝑝𝑎𝑟𝑡)

𝐼

+ 𝑘 ℎ𝑦𝑑 (𝑝𝑎𝑟𝑡)

𝐼

), therefore, all values presented below only refer to ozone degradation.

Heterogeneous ozonolysis

In order to evaluate the influence of humidity on the heterogeneous reaction rates of pesticides, ozonolysis experiments were conducted at relative humidity level between 0% and 80% RH for the three kinds of particles, i.e., hydrophobic silica, hydrophilic silica, and Arizona dust.

0% RH is an unrealistic value as water is always present in the atmosphere. However, most studies of the heterogeneous reactivity of pesticides toward ozone were carried out closer to 0% RH [START_REF] Pflieger | Kinetic Study of Heterogeneous Ozonolysis of Alachlor, Trifluralin and Terbuthylazine Adsorbed on Silica Particles under Atmospheric Conditions[END_REF][START_REF] Pflieger | The Heterogeneous Ozonation of Pesticides Adsorbed on Mineral Particles: Validation of the Experimental Setup with Trifluralin[END_REF][START_REF] Pflieger | Ozonation of isoproturon adsorbed on silica particles under atmospheric conditions[END_REF][START_REF] Segal-Rosenheimer | Heterogeneous Oxidation of the Insecticide Cypermethrin as Thin Film and Airborne Particles by Hydroxyl Radicals and Ozone[END_REF]. From the analysis of water adsorption on the surface of mineral oxides, [START_REF] Goodman | Spectroscopic Study of Nitric Acid and Water Adsorption on Oxide Particles: Enhanced Nitric Acid Uptake Kinetics in the Presence of Adsorbed Water[END_REF] have shown that the number of water layers is approximately one monolayer at 20% RH, two to three adsorbed water layers at 50% RH, and three to four at 85% RH. 80% RH seems to be a realistic level where the aerosol is close to the state of a deliquescent aerosol.

Under these experimental conditions, tetraconazole, fipronil, oxadiazon, and difenoconazole,

were not or slightly degraded (𝑘 𝑂 3(𝑝𝑎𝑟𝑡)

𝐼𝐼

≤ 10 -20 cm 3 molecule -1 s -1 ; t½ ≥ 800 days) whatever the nature of particles. On the other hand, cyprodinil, deltamethrin, permethrin, and pendimethalin, showed significant losses due to ozone exposure when adsorbed on all three particle types.

Second-order rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 ranged from (4.7 ± 0.4) × 10 -20 cm 3 molecule -1 s -1 (pendimethalin, hydrophobic silica, 55% RH) to (2.3 ± 0.4) × 10 -17 cm 3 molecule -1 s -1 (cyprodinil, Arizona dust, 0% RH). The order of magnitude of these constants are in accordance with previous pesticide heterogeneous ozonolysis studies conducted on silica particles [START_REF] Socorro | Heterogeneous Reactions of Ozone with Commonly Used Pesticides Adsorbed on Silica Particles[END_REF] and reference therein), quartz surfaces (Al [START_REF] Rashidi | The heterogeneous photo-oxidation of difenoconazole in the atmosphere[END_REF][START_REF] Rashidi | Heterogeneous Ozonolysis of Folpet and Dimethomorph: A Kinetic and Mechanistic Study[END_REF][START_REF] El Masri | A mechanistic and kinetic study of the heterogeneous degradation of chlorpyrifos and chlorpyrifos oxon under the influence of atmospheric oxidants: ozone and OH-radicals[END_REF][START_REF] Bouya | Kinetics of the Heterogeneous Photo Oxidation of the Pesticide Bupirimate by OH-Radicals and Ozone under Atmospheric Conditions[END_REF], ZnSe crystals (Segal-Rosenheimer and Dubowski, 2007), azelaic acid aerosols [START_REF] Gan | Products and kinetics of the heterogeneous reaction of suspended vinclozolin particles with ozone[END_REF][START_REF] Meng | Heterogenous ozonation of suspended malathion and chlorpyrifos particles[END_REF][START_REF] Yang | Heterogeneous Reactivity of Suspended Pirimiphos-Methyl Particles with Ozone[END_REF]Yang et al., , 1012)), and grape berries [START_REF] Walse | Remediation of Fungicide Residues on Fresh Produce by Use of Gaseous Ozone[END_REF].

It may also be noted that both pyrethroids (deltamethrin and permethrin) are degraded by ozone, probably due to an attack of ozone on the alkene double bond leading to the formation of a primary ozonide (Socorro et al., 2016b), while no significant degradation is observed in our experimental conditions for both triazoles (difenoconazole and tetraconazole). These results show the effect of the chemical structures on pesticide reactivity.

Influence of humidity

Fig. 3 represents the variation of the second-order rate constants in function of relative humidity for the four pesticides which showed significant losses by ozone exposure, i.e., cyprodinil, deltamethrin, permethrin, and pendimethalin, on all three particles types.

Fig. 3: Second-order rate constants for the ozonolysis of pesticides adsorbed on hydrophobic silica, hydrophilic silica, and Arizona dust at different relative humidity level (▲:

Hydrophilic silica; : Hydrophobic silica; : Arizona Dust)

To characterize the influence of RH, the ratio between the lowest and the highest 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 obtained at different RH was calculated for each pesticide adsorbed on each particle type.

Hydrophilic silica

Second-order rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 on hydrophilic silica ranged from (2.3 ± 1.4) × 10 -19 cm 3 molecule -1 s -1 (cyprodinil, 80% RH) to (4.1 ± 0.4) × 10 -18 cm 3 molecule -1 s -1 (pendimethalin, 5% RH). The four pesticides exhibit the same trend, characterized by a decrease of their reactivity constant at high relative humidity. For all pesticides, the maximum ratio was obtained and 5% RH were not significantly different for all pesticides. Considering these ratios, deltamethrin, permethrin, and cyprodinil reacted 3, 4, and 4 times faster at 5% RH than at 80% RH, respectively. For pendimethalin, 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 varied between (3.3 ± 0.8) × 10 -19 cm 3 molecule - 1 s -1 (80% RH) and (4.1 ± 0.4) × 10 -18 cm 3 molecule -1 s -1 (5% RH), which corresponds to a degradation 12 times faster when the humidity was low.

Hydrophobic silica

Second-order rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 ranged from (4.7 ± 0.4) × 10 -20 cm 3 molecule -1 s -1 (pendimethalin, 55% RH) to (2.6 ± 0.2) × 10 -18 cm 3 molecule -1 s -1 (cyprodinil, 0% RH). For the four pesticides, the highest 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 was obtained at 0% RH. As observed for hydrophilic silica particles, pesticides reacted slower when the relative humidity increased. The maximum ratios obtained between the extreme 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 were close to those obtained for hydrophilic silica.

Deltamethrin, permethrin, cyprodinil, and pendimethalin reacted 2, 2, 3, and 16 times faster at the lowest relative humidity, respectively. For deltamethrin and permethrin, 𝑘 𝑂 3(𝑝𝑎𝑟𝑡)

𝐼𝐼

were not significantly different between 0% and 80% RH, despite a significant variation with the intermediate RH levels.

Arizona dust

𝑘 𝑂 3(𝑝𝑎𝑟𝑡)

𝐼𝐼 measured for Arizona dust were characterized by poor reproducibility, within a range of RSD from 3% to 234%. The difficulty to correctly assess the kinetic constants is potentially due to the ozone degradation on particles surfaces inducing a slow drift of its concentration throughout the experiments. Indeed, during the 26h of experiment, the ozone mixing ratio decreased continuously and could vary up to 33%. This important drift can be compared to those obtained for hydrophobic and hydrophilic silicas that is lower than 4%. This behavior can be associated to the chemical composition of the particles since silica particles contains mainly SiO2 (> 99.8wt%) while Arizona dust contains silica but also significant wt% of Al2O3 and Fe2O3). Those results are in agreement with previous studies [START_REF] Michel | Reactive Uptake of Ozone on Mineral Oxides and Mineral Dusts[END_REF]Usher et al., 2003) which showed that the relative reactivity of ozone followed the trend Fe2O3 > Al2O3 > SiO2. Anyway, the important RSD observed for Arizona particles makes it difficult to conclude about the influence of humidity on deltamethrin, permethrin, and pendimethalin for which no significant variation of 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 was observed. For cyprodinil, 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 varied by two orders of magnitude between dry conditions, i.e., (2.3 ± 0.3) × 10 -17 cm 3 molecule -1 s -1 (0% RH) and humid conditions, i.e., (0.9 ± 2.2) × 10 -17 cm 3 molecule -1 s -1 (30% RH) and (2.3 ± 0.1) × 10 -19 cm 3 molecule -1 s -1 (80% RH).

Overall, whatever the nature of the mineral particles, when an RH effect was observed, the same trend was observed in this work. The more the RH increased, the slowest the heterogeneous ozonolysis was. The influence of humidity on the heterogeneous ozonolysis degradation was already investigated for instance for PAH on many surfaces [START_REF] Pitts | Factors Influencing the Reactivity of Polycyclic Aromatic Hydrocarbons Adsorbed on Filters and Ambient POM with Ozone[END_REF][START_REF] Pöschl | Interaction of Ozone and Water Vapor with Spark Discharge Soot Aerosol Particles Coated with Benzo[a]pyrene: O3 and H2O Adsorption, Benzo[a]pyrene Degradation, and Atmospheric Implications[END_REF][START_REF] Kwamena | Kinetics of Surface-Bound Benzo[END_REF]. To our knowledge, only [START_REF] Segal-Rosenheimer | Heterogeneous Ozonolysis of Cypermethrin Using Real-Time Monitoring FTIR Techniques[END_REF] have worked on the heterogeneous ozonolysis of cypermethrin, a pyrethroid insecticide, adsorbed on ZnSe crystals and, to a lesser extent, the influence of the humidification rate on ozonation was investigated for seeds containing pesticides [START_REF] Bourgin | Study of the Degradation of Pesticides on Loaded Seeds by Ozonation[END_REF].

In their study, [START_REF] Pitts | Factors Influencing the Reactivity of Polycyclic Aromatic Hydrocarbons Adsorbed on Filters and Ambient POM with Ozone[END_REF] exposed five PAH adsorbed on glass fiber (GF) and Teflon impregnated glass fiber (TIGF) filters to 200 ppb of ozone at 1, 25 and 50% RH (ambient temperature). They observed a "humidity effect" with a decrease in reactivity at high RH and concluded to a competition between water and ozone for adsorptive sites. In the same way, [START_REF] Pöschl | Interaction of Ozone and Water Vapor with Spark Discharge Soot Aerosol Particles Coated with Benzo[a]pyrene: O3 and H2O Adsorption, Benzo[a]pyrene Degradation, and Atmospheric Implications[END_REF] observed the decrease of benzo[a]pyrene (BaP) decay rates toward ozone (0-1 ppm) on soot aerosols in the presence of water in the range from 0% to 25% RH at 23°C. In addition, they indicated that an increase of RH beyond 50% may not lead to further reduced reaction rates [START_REF] Pöschl | Formation and Decomposition of Hazardous Chemical Components Contained in Atmospheric Aerosol Particles[END_REF]. They also suggested a competitive adsorption of ozone and water on the surface. For both studies, this assumption was supported by the nonlinear fits between pseudo first-order rate constants and ozone concentrations, suggesting a L-H mechanism, i.e., the gas-phase ozone is adsorbed on the particle surface prior to the reaction with the adsorbed compounds. Hence, it involves that at high ozone concentration, the relative humidity has less influence on chemical lifetime.

In contrast to the behavior on soot aerosols and GF and TIGF filters, Segal-Rosenheimer and Dubowski ( 2007) observed no significant difference on the heterogeneous ozonolysis reactivity (30 ppb -60 ppm) of the insecticide cypermethrin adsorbed on ZnSe crystals at ~7% and ~80% RH. Moreover, [START_REF] Kwamena | Kinetics of Surface-Bound Benzo[END_REF] mentioned the opposite effect, that is, at high RH (~72% at 25°C) the ozonolysis kinetics were faster than at low RH (<1%) for BaP on azelaic acid aerosols. Even if the influence of the humidity has not the same trend as previous studies, [START_REF] Kwamena | Kinetics of Surface-Bound Benzo[END_REF] emphasized the role of the surface. Thus, it appears that the influence of the relative humidity on the heterogeneous reactivity should be linked with the nature of particles where pesticides under study were adsorbed.

Influence of the particle type

Fig. 4 presents the second-order rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 of cyprodinil, deltamethrin, pendimethalin, and permethrin for the three particle types under study in function of relative humidity. [START_REF] Perraudin | Kinetic Study of the Reactions of Ozone with Polycyclic Aromatic Hydrocarbons Adsorbed on Atmospheric Model Particles[END_REF] have shown no significant kinetic difference during heterogeneous ozonolysis of several PAH adsorbed on various silica particles (same hydrophilic surface chemistry, different particle diameters (5 and 40 µm), pore sizes (70 and 200 Å), and specific surface areas (200 and 500 m 2 g -1 )). In order to evaluate the influence of the hydrophobicity/hydrophilicity of the surface of particles, both synthetic silicas were chosen with the same particle size and the same specific surface area. In the present work, only the surface chemistry can be considered to be different as silanol groups have a hydrophilic nature whereas the siloxane groups are chemically inert and hydrophobic. In addition, Arizona dust particles were chosen to be an atmospheric mineral model of particles but, as Saharan sand or Gobi dust [START_REF] Perraudin | Kinetic Study of the Reactions of Ozone with Polycyclic Aromatic Hydrocarbons Adsorbed on Atmospheric Model Particles[END_REF], their specific surface area was much lower than both synthetic silicas (one order of magnitude here).

According to their reactivity toward ozone, pesticides under study can be split in two categories whether they were more reactive on hydrophilic or on hydrophobic silica particles. Fig. 4: Second-order rate constant for the degradation of pesticides adsorbed on hydrophobic silica, hydrophilic silica, and Arizona dust by ozone Pendimethalin, deltamethrin, and permethrin showed the same pattern, that is, at low RH (0% and 30%), the reactivity was from 2 to 8 times faster on hydrophilic particles than on hydrophobic particles whereas at 80% RH, there was no significant difference. The secondorder rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 were the same on Arizona dust and hydrophobic silica particles at 0% and 30% RH, partly due to the high RSD of 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 for Arizona dust. However, at 80% RH, the reactivity was faster on Arizona dust of a factor of about 2-3 than on synthetic silicas.

Thus, the nature of the particle appears to influence the reactivity of pesticides toward ozone.

At 0% RH, in the absence of competition between ozone and water for adsorption, the difference in reactivity for pesticides adsorbed on hydrophobic and hydrophilic silica particles suggests a greater affinity of ozone for hydrophilic surface mainly composed by silanol groups.

At 30% RH, the amount of water adsorbed on particles increases mainly on hydrophilic particles because of the presence of hydroxyl groups on their surfaces, i.e., silanol groups [START_REF] Vigil | Interactions of Silica Surfaces[END_REF][START_REF] Muster | Water Adsorption Kinetics and Contact Angles of Silica Particles[END_REF][START_REF] Verdaguer | Growth and structure of water on SiO2 films on Si investigated by Kelvin probe microscopy and in situ Xray Spectroscopies[END_REF]. It should be noted that the rehydroxylation of the hydrophobic siloxane surface in presence of wet air is possible, but it is a slow process. Nevertheless, the reactivity on hydrophilic surface remained higher than on hydrophobic surface, suggesting that the amount of water remains too low to induce a competitive adsorption between ozone and water for particle surfaces. At 80% RH, when silica is fully hydrated, all siloxane groups link with water to form silanol groups [START_REF] Muster | Water Adsorption Kinetics and Contact Angles of Silica Particles[END_REF], which leads to a similar reactivity on both synthetic silicas.

Unlike the other 3 pesticides (deltamethrin, pendimethalin, and permethrin), cyprodinil was more reactive on hydrophobic silica than on hydrophilic silica of a factor of about 2-4 whatever the RH. Moreover, cyprodinil showed the highest reactivity with 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 = (2.3 ± 0.3) × 10 -17 cm 3 molecule -1 s -1 at 0% RH when adsorbed on Arizona dust. However, it should be kept in mind that the specific surface area of Arizona dust particles is about one order of magnitude lower than that of synthetic silicas. Therefore, the percentage of pesticide coating during these ozonolysis exposure was higher for Arizona dust. Complementary experiments will be needed to know the influence of the concentration of adsorbed pesticides on particles.

These differences in kinetic behavior between pendimethalin, deltamethrin, and permethrin on the one hand and cyprodinil on the other, seem to highlight that the chemical nature of the pesticide is also a factor to consider during the heterogeneous ozonolysis.

Nature of the adsorbed pesticide and comparison with other studies

The different reaction rate constants of heterogeneous ozonolysis and their associated atmospheric half-lives are summarized by chemical family of pesticides under study and compared to literature data [START_REF] Meylan | Computer estimation of the Atmospheric gas-phase reaction rate of organic compounds with hydroxyl radicals and ozone[END_REF][START_REF] Pflieger | Kinetic Study of Heterogeneous Ozonolysis of Alachlor, Trifluralin and Terbuthylazine Adsorbed on Silica Particles under Atmospheric Conditions[END_REF][START_REF] Pflieger | The Heterogeneous Ozonation of Pesticides Adsorbed on Mineral Particles: Validation of the Experimental Setup with Trifluralin[END_REF][START_REF] Yang | Heterogeneous Reactivity of Suspended Pirimiphos-Methyl Particles with Ozone[END_REF][START_REF] Yang | Heterogeneous Ozonolysis of Pirimicarb and Isopropalin: Mechanism of Ozone-Induced N-Dealkylation and Carbonylation Reactions[END_REF][START_REF] Walse | Remediation of Fungicide Residues on Fresh Produce by Use of Gaseous Ozone[END_REF][START_REF] Bourgin | Study of the Degradation of Pesticides on Loaded Seeds by Ozonation[END_REF][START_REF] Bouya | Kinetics of the Heterogeneous Photo Oxidation of the Pesticide Bupirimate by OH-Radicals and Ozone under Atmospheric Conditions[END_REF] in Table 1.

Even though no degradation was observed in our conditions for tetraconazole and difenoconazole, two triazole fungicides, several studies were carried out to remove triazole adsorbed on the surface of plants. However, the ozonation process frequently requires high ozone concentration. Heleno et al. (2013) investigated the effect of ozone fumigation on the reduction of difenoconazole residue on strawberries. Difenoconazole was removed up to 95% after 1h when exposed to 400 ppm of ozone. [START_REF] Bourgin | Study of the Degradation of Pesticides on Loaded Seeds by Ozonation[END_REF] exposed seeds coated by the triazole bitertanol at very high ozone concentration (51,000 ppm). The half-lives calculated from the rate constants reported in literature agree with the present study and confirm that triazole fungicides were not affected by ozonolysis at atmospheric concentrations.

Several ozonolysis studies dealt with the compounds of the pyrimidine family adsorbed on various surfaces without ever specifying the relative humidity. Our results are in accordance with those obtained for pyrimethanil, pirimiphos-methyl, and bupirimate adsorbed on model atmospheric aerosols [START_REF] Yang | Heterogeneous Reactivity of Suspended Pirimiphos-Methyl Particles with Ozone[END_REF][START_REF] Bouya | Kinetics of the Heterogeneous Photo Oxidation of the Pesticide Bupirimate by OH-Radicals and Ozone under Atmospheric Conditions[END_REF]. However, ozonation studies performed on surface of grape berries exhibit half-lives much higher [START_REF] Walse | Remediation of Fungicide Residues on Fresh Produce by Use of Gaseous Ozone[END_REF].

The same hydrophobic silica particles were used to study the heterogeneous ozonolysis of dinitroaniline herbicides [START_REF] Pflieger | Kinetic Study of Heterogeneous Ozonolysis of Alachlor, Trifluralin and Terbuthylazine Adsorbed on Silica Particles under Atmospheric Conditions[END_REF][START_REF] Pflieger | The Heterogeneous Ozonation of Pesticides Adsorbed on Mineral Particles: Validation of the Experimental Setup with Trifluralin[END_REF][START_REF] Yang | Heterogeneous Ozonolysis of Pirimicarb and Isopropalin: Mechanism of Ozone-Induced N-Dealkylation and Carbonylation Reactions[END_REF]. Half-lives of pendimethalin, trifluralin, and isopropalin were of the same order of magnitude, suggesting that the kinetic data obtained for one pesticide can be extended to the whole chemical family, here, the dinitroaniline family. Moreover, the same results were obtained for both pyrethroid insecticides whatever the particle types, suggesting again a generalization to a whole chemical family. It should also be noted that the kinetic data of the theoretical gas-phase ozonolysis for both pyrethroids under study [START_REF] Meylan | Computer estimation of the Atmospheric gas-phase reaction rate of organic compounds with hydroxyl radicals and ozone[END_REF] exhibits the same order of magnitude as the experimental ozonolysis kinetics rate constants in the particulate phase. a Atmospheric half-lives calculated for [𝑂 3(𝑔𝑎𝑠) ] = 40 ppb [START_REF] Vingarzan | A review of surface ozone background levels and trends[END_REF].

Atmospheric implications

The heterogeneous ozonolysis yields to deltamethrin, permethrin, cyprodinil, and pendimethalin degradation. However, whatever the atmospheric conditions of humidity and nature of particles, difenoconazole, tetraconazole, fipronil, and oxadiazon will present no degradation towards ozone. Indeed, unlike to deltamethrin and permethrin (alkene double bond) and cyprodinil and pendimethalin (secondary amine group), they have no chemical groups likely to react with ozone. Consequently, the calculated atmospheric half-lives (Table 1) for an ozone mixing ratio of 40 ppb, which is representative of the atmospheric ozone level in mid latitudes of the Northern hemisphere [START_REF] Vingarzan | A review of surface ozone background levels and trends[END_REF], are higher than several years.

Moreover, Socorro et al. (2016a) also reported that difenoconazole, tetraconazole, fipronil, and oxadiazon were not degraded by hydroxyl radicals in particulate phase which implies a significant persistence of these pesticides in the atmosphere once adsorbed on particles.

The half-life of cyprodinil can widely range from a few hours to several months, and from a few hours to several weeks for pendimethalin, permethrin, and deltamethrin. These half-lives are also significant enough to involve a transport over long distances prior to be removed and a potential transfer to aquatic and terrestrial ecosystems where they can cause hazard effects.

Hence, from a legislative point of view, according to the Stockholm convention, these pesticides can be considered as persistent organic compounds (POPs) in the atmosphere with respect to the gas-phase ozone (UNEP, 2001).

However, given the complexity of the surfaces of atmospheric particles and the atmospheric variation of relative humidity, the heterogeneous ozonolysis can be considered as a very slow process for the studied pesticides compared with the highly reactive hydroxyl radicals (Socorro et al., 2016a).

Conclusions

Kinetic data are dependent on relative humidity, on particles surface chemistry, and chemical nature of the adsorbed pesticides. For the four reactive pesticides (i.e., cyprodinil, deltamethrin, permethrin, and pendimethalin), heterogeneous ozonolysis reactions are slower at high relative humidity suggesting a competitive adsorption of ozone and water on particle surface.

Moreover, reactivity on hydrophilic surface are faster than on hydrophobic surface in the absence of water and at low RH for deltamethrin, permethrin, and pendimethalin. When RH increases (i.e., 80% RH), pesticides exhibit comparable reactivity on both synthetic silicas, suggesting a rehydroxylation of the hydrophobic siloxane surface in presence of wet air.

However, the opposite kinetic behavior observed for cyprodinil also implies the influence of the chemical nature of pesticide. Pesticides of the same chemical family (deltamethrin/permethrin and difenoconazole/tetraconazole) appear to have the same kinetic behaviour, suggesting a possible generalization of the kinetic results to the whole chemical family.

These results suggest that relative humidity must be taken into account to determine kinetic rate constants and that studies carried out at 0% RH cannot be considered as representative of the atmospheric conditions. Finally, given the chemical structures of pesticides and the complexity of atmospheric particles surface, it is currently difficult to predict degradation kinetics as may be the case for the gas-phase.

Fig. 1 :

 1 Fig. 1: Observed pseudo-first order rate constants 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼

Fig. 2 :

 2 Fig.2: First order kinetic constants for 8 pesticides adsorbed on hydrophobic silica,

  and 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 at 5% RH. It should be noted that 𝑘 𝑂 3(𝑝𝑎𝑟𝑡) 𝐼𝐼 at 0%

Table 1 :

 1 Kinetic data for the ozonolysis of the adsorbed pesticides (in bold) under study and atmospheric half-lives compared to the literature

	data

Acknowledgement

This work has been carried out thanks to the support of the COPP'R project "Modelling of atmospheric contamination by plant protection products at the regional scale" funded by the PRIMEQUAL -AGRIQA « Agriculture et qualité de l'air » program. C. Mattei received a


Olivier Llopis
email: llopis@laas.fr

Sébastien Gribaldo

Cédric Chambon

Bertrand Onillon

Jean-Guy G Tartarin

Laurent Escotte

Recent evolutions in low phase noise microwave sources and related

Keywords: microwave oscillator, frequency generation, phase noise, nonlinear noise PACS: 43.58.Wc

INTRODUCTION

Spectrally pure frequency generation is necessary in many applications. Precision timing, as an example, is directly related to the source phase noise. More generally, in many physics applications, the frequency is the parameter on which the highest constraints are put on. However, the strongest economical challenge in this field is today for telecommunications applications. The phase noise of the oscillator is indeed superimposed directly to the signal when this signal is demodulated or simply converted in frequency. Thus, the oscillator noise close to the carrier becomes the limit of the signal to noise ratio at the receiver output. Of course, different types of oscillators are used in physics or telecommunications applications. Physicists are mainly seeking performance meanwhile the telecommunications industry needs small size and low cost systems, which means a high level of integration. However, the theoretical description of the noise mechanisms in these systems is very similar, even if the frequency reference element (the resonator) is different. Another application field, which could be located between the two previous ones, is the development of highly sensitive radars or telemeters. This is of high interest for military purpose, but not only. In these applications, both high performance and small size are needed, which is of course difficult to achieve.

Because of these different application fields, research on high spectral purity oscillators is performed in different scientific communities : the time and frequency community first ; secondly the microwave community, which drives research for both telecommunications and military applications ; then the circuit community, which is also related to the telecommunications field, and which is focused on integrated sources. The last community is of course the one of noise. Indeed, the investigations on phase noise, and particularly the pioneering work performed in the microwave field [START_REF] Siweris | A GaAs FET oscillator noise model with a periodically driven noise source[END_REF][START_REF] Rizzoli | [END_REF][3][START_REF] Llopis | Nonlinear noise modeling of a PHEMT device through residual phase noise and low frequency noise measurements[END_REF], have revealed some theoretical problems related to the description of noise under nonlinear conditions. It was thus mandatory to think again the transistor noise modeling, which had been developed for linear applications, and to adapt this modeling to the description of a nonlinear problem. Of course, the device modeling is only one part of the problem, the other one being the development of powerful CAD tools, able to compute the phase noise from these models in an complex circuit. Such tools have been developed in the 1990s [START_REF] Rizzoli | [END_REF], and the problem of the noise transposition in a nonlinear circuit between the different harmonics is now well described by these approaches. However, the effect of the nonlinear signal on the noise source itself is still a disputed subject. This problem will be discussed in this paper.

Describing the oscillator phase noise through the behavior of the transistor noise under nonlinear conditions is valid, providing the other elements of the oscillator do not contribute too much to the oscillator noise. In this case, it is possible to improve the oscillator performance finding out the appropriate transistor load at each harmonics which minimizes the overall output phase noise. This approach can be efficient even if the complete noise generation process at the transistor level is not completely understood. However, for some applications it is mandatory to be able to simulate the oscillator phase noise with a high precision (because the circuit cannot be tuned after being realized). In this case, a model able to precisely describe the noise under nonlinear conditions is required.

The problem discussed in the above paragraph is the one of any microwave circuit using only passive elements for frequency reference: integrated LC oscillators and VCOs, dielectric resonator or coaxial resonator oscillators, sapphire oscillators… However, if the resonator itself is not passive, it may be the predominant contribution to the output phase noise. This is the case of acoustic wave resonators, which feature a 1/f fluctuation of their resonant frequency. Also, very recently, it has been proposed to use optical delay lines as the frequency reference elements of microwave oscillators. However, in this case also, the signal conversion to optics add its noise contribution, which must be evaluated.

MODELING OF OSCILLATORS WITH PASSIVE RESONATORS

As described in Leeson's paper [START_REF] Leeson | Proc. of the IEEE[END_REF], an oscillator is a feedback loop with a phase fluctuating amplifier and a resonator in the feedback. The amplifier phase noise is directly converted through the loop effect into the oscillator's frequency noise. Investigating the phase noise of the amplifier is simpler than investigating on the complete oscillator, because : 1) there is no phase loop condition, so the measurement can be performed in well defined conditions 2) the measurement can be performed on a large RF power range 3) it is easier and faster to simulate the performance of a driven circuit than an autonomous circuit 4) It is essential to investigate the noise conversion processes independently of the surrounding circuit. To this purpose, a measurement bench has been developed [START_REF] Cibiel | [END_REF] which is able to characterize this parameter, either on an already designed amplifier or on a single transistor on which both the RF and LF loads are controlled. The goal of these measurements is to study the correlation between the transistor low frequency (LF) noise and the transistor phase noise. The transistor LF noise should therefore be measured in the same operating conditions i.e. submitted to the nonlinear signal. This is performed on the same measurement bench, adding an output on the device bias Tees and a control of the device LF loads (Figure 2).

An example of the data obtained with this measurement bench is given in Figure 3. The microwave power at 3.5 GHz is smoothly increasing from the linear regime up to 4 dB compression. The change in the spectral shape between the linear behavior and the nonlinear behavior is strong, and the noise in the nonlinear behavior can hardly be predicted using the linear (or quiescent) data. However, is obviously a strong correlation between the LF noise and the phase noise, which means that a global modeling able to describe simultaneously these too spectrum sets could be extracted. The model which had been proposed for this device [START_REF] Llopis | Nonlinear noise modeling of a PHEMT device through residual phase noise and low frequency noise measurements[END_REF] involved to main LF noise sources, one of which (a g.r. noise source) taking advantage on the other one when the device was driven far in the nonlinear state. In this model, the nonlinear behavior of this g.r. noise source had been described through the association of this noise source with a nonlinear element, which was introduced in the device electrical model mainly to fit the measurement rather than because it had a physical meaning. Other authors argued that the noise source itself could be treated as a nonlinear element. This has been proposed as early as the first experiments [START_REF] Siweris | A GaAs FET oscillator noise model with a periodically driven noise source[END_REF], and the more recent papers on this subject seems to be in favor of this approach [START_REF] Bonani | [END_REF][9][10][11]. However, an equivalent circuit modeling remains a rough approximation of the transistor behavior, contrarily to physical modeling. A good model, at this level of approximation, is simply a model which is able to describe the measurement, at various input power levels or for different transistor load. So if good results can be obtained with a noise source instantaneously sensitive to the microwave signal, and there are some physical arguments that the noise could behave in this way, this approach should become the standard approach to model the noise in nonlinear circuits. Frequency (Hz) Phase Noise (dBrad/Hz) P in FIGURE 3. Example of data obtained on a FET device [START_REF] Llopis | Nonlinear noise modeling of a PHEMT device through residual phase noise and low frequency noise measurements[END_REF] ; left : equivalent input voltage noise spectral density at different microwave power levels (P in ) ; right : phase noise at 3.5 GHz, the transistor being loaded onto 50 Ω at RF, for the same range in RF power (P in )

We have thus used this approach to model the phase noise generated by a SiGe HBT. We will not describe in details this model here, because it is presented in a focused paper in these proceedings [START_REF] Gribaldo | Nonlinear noise in SiGe bipolar devices and its impact on radio-frequency amplifier phase noise[END_REF]. It is an improvement of a simpler model which was using external noise sources parameterized by the microwave power [13]. This technique, which uses power dependant external LF noise sources, is very efficient, but it requires that the noise parameters are measured on an amplifier which is close to the one which will be used in the final oscillator circuit. It allows anyway some phase noise optimization, and as proven its efficiency on the design of high spectral purity sources [START_REF] Cibiel | [END_REF]. The new model is no more based on an extrinsic parameter. On the contrary, the nonlinear behavior arises from an instantaneous dependence of the collector current noise spectral density S ic to the RF signal. S ic is supposed to be composed of a constant coefficient and of a second term proportional to i c 2 (t). In the commercial circuit design software (Agilent ADS) used to simulate the phase noise, this noise source is considered just like a classical nonlinear element, using a symbolically defined device. The parameters of this new type of nonlinearity are extracted from the measurement of the equivalent input LF noise at different RF power levels [START_REF] Gribaldo | Nonlinear noise in SiGe bipolar devices and its impact on radio-frequency amplifier phase noise[END_REF]. Other authors use to this purpose multi-bias noise measurements [10,11], but we think that the measurement of noise under nonlinear conditions is closer to the final behavior of the transistor and is more reliable for the extraction of the noise nonlinear behavior.

The above discussion is focused on the effect on phase noise of the device LF noise. However, phase noise is the fluctuation of a high frequency signal, an even if close to the carrier this fluctuation is dominated by the LF fluctuations (1/f or g.r. noise), far from the carrier it can be the result of the superposition of microwave noise. These two behaviors are described as multiplicative (or conversion) noise and additive noise [15]. The additive noise is a carrier to noise ratio, and is thus almost inversely proportional to the RF signal level. On the contrary, the multiplicative noise comes from a modulation or conversion process, and follows the signal level. The microwave noise has an advantage compare to the 1/f noise : it is generally well localized in the transistor model (thermal noise of the resistances, schottky noise in the junctions). However, it is also affected by the nonlinear behavior, and the classical approach which involves the transistor noise figure is no more valid, unless a nonlinear noise figure can be simulated or measured [15]. This last noise contribution can be simulated using modern CAD tools or, also, can be investigated experimentally in a relatively similar way which is used to find the minimum noise figure of an amplifier. A focused paper on such an approach can be found in this volume [16].

NOISE PROBLEMS IN MICROWAVE SOURCES USING ACTIVE FREQUENCY REFERENCE ELEMENTS

The evolution of microwave sources has introduced recently some new problems of noise modeling. Firstly, the telecommunications industry needs today highly integrated high quality sources, and has succeeded very recently in this field thanks to a new device : the integrated thin film bulk acoustic wave resonator. This resonator is an integrated version of the quartz resonator, and it is able to provide a Q factor of 10 2 to 10 3 in the low microwave range (1 to 5 GHz). Integrated oscillators based on this resonator feature a much better performance than classical LC based VCOs [START_REF] Aissi | A 5.4 GHz 0.35um BiCMOS FBAR resonator oscillator in above-IC technology[END_REF]. However, the performance of these sources is limited by an intrinsic 1/f fluctuation of the resonator frequency, which appears to be higher than the effect of the transistor phase noise [START_REF] Gribaldo | [END_REF]. Up to the author's knowledge, no modeling approach has been proposed for this frequency fluctuation, or at least no modeling approach which could be embedded in a circuit simulator. Investigations on this type of noise, and on integrated acoustic wave resonator oscillators, are the key of success for the development of the next generation of small volume microwave sources.

On the other of oscillators applications, where high performance is the main goal, optical techniques are today foresee to design very high spectral purity microwave sources. In this case, the microwave signal is transferred to the optical range thanks to an optical carrier. Once in the optical domain, it is possible to take benefit of the ultra low losses of the optical delay lines which can trap the signal in a few kilometers line with almost no attenuation, except the one due to the microwave to optical (MO) and optical to microwave (OM) conversions. The equivalent Q factor is very high, and high performance oscillators [START_REF] Yao | Progress in the optoelectronic oscillator -a ten year anniversary review[END_REF] or phase noise measurement benches [START_REF] Onillon | Optical links for ultra-low phase noise microwave oscillators measurement[END_REF] have been realized with this technique. One of the drawbacks is in the size required for a few kilometers fiber optics delay line. To overcome this problem, it has been proposed to replace the line by an optical resonator, but this is difficult and still under study. One of the problems of these systems is the carrier to noise degradation due to the MO and OM conversions. This carrier to noise ratio is determined by the efficiency of the optical modulation or detection, and by the laser relative intensity noise (RIN). The last parameter may also influence the close to carrier phase noise because of the laser 1/f RIN. Simulating the overall noise behavior of such a system is difficult, and up to now only analytical approaches have been proposed. The goal is now to develop models and CAD tools able to manage the noise simultaneously in RF and optical devices, in order to optimize these new hybrid systems.

CONCLUSION

Reducing the phase noise of a high frequency oscillator is one of today's more difficult modeling problems in electronics. This is because it requires an accurate description of the noise under nonlinear behavior. Experimental approaches have been described to check the validity of the various modeling approaches, and a focus is made on models involving nonlinear noise sources. Finally, the problem of noise studies of more complex sources involving resonances which are not entirely of electrical type is pointed out. All these systems still requires investigations in the field of noise modeling.

FIGURE 2 .

 2 FIGURE 2. Details of the part of the experiment used to investigate on the device LF noise under nonlinear signal conditions.

  Residual phase noise (or amplifier phase noise) measurement bench, which is able to perform phase noise measurements on the 1 to 18 GHz range (using different low FM noise sources)

							FFT analyser FFT analyser
	Faraday's shielding + battery bias Faraday's shielding + battery bias							. .
								A B LFG A B LFG A B LFG
	Low FM and AM noise source Low FM and AM noise source
	Att Att Att Att	Att Att Att Att	DUT DUT DUT DUT	Att Att Att Att	φ φ φ φ φ φ	RF RF	Dual Φ detector Dual Φ detector
	AM limiter AM limiter						X X X X	A LF A LF
						OL OL
	Synthesised source with AM capabilities Synthesised source with AM capabilities					X X X X	A LF A LF
	for AM minimization for AM minimization
								LF signal LF signal
	Measurement performed in a Faraday's shield Measurement performed in a Faraday's shield FIGURE 1. FFT Battery bias Battery bias Rc Battery bias Battery bias Rc analyser LNA Rb analyser LNA FFT Rb
	P in P in	> 20 μF > 20 μF					~ 20 μF ~ 20 μF
	Att Att