V Szczepan

F Brix

C Petitjean

P J Panteix

M Vilasi

A new modeling of the dissolution of chromia in Na2O-SiO2 liquids

Keywords: glass, chromia, dissolution, thermochemistry, modeling, numerical simulation

A model of dissolution of chromia in binary Na2O-SiO2 liquids is presented in this work.

Data available in the literature on the acid/base properties and the chemistry of chromium in such liquids were used in order to refine the model. Physical phenomena such as migration of ions and the resulting electric field, the mechanical equilibrium of the liquid and the interface recession caused by the dissolution of chromia are also implemented in the model. Numerical simulation has been compared to experimental measurements of Na2O, SiO2 and Cr2O3 concentration profiles after 1 hour of immersion of chromia in a Na O . SiO . liquid at 1150 °C. The phenomena having a significant influence on the dissolution rate of chromia are highlighted in the last part of this paper.

List of symbols

Introduction

The contact between an alloy and a silica-based liquid at high temperature is a commonly encountered issue in glass industries such as nuclear waste vitrification [START_REF] Sengupta | Interaction study between nuclear waste-glass melt and ceramic melter bellow liner materials[END_REF] or glass fiber production [START_REF] Martino | Corrosion of metals and alloys in molten glasses. Part 1: glass electrochemical properties and pure metal (Fe, Co, Ni, Cr) behaviours[END_REF][START_REF] Martino | Corrosion of metals and alloys in molten glasses. Part 2: nickel and cobalt high chromium superalloys behaviour and protection[END_REF]. Nickel-based or cobalt-based super-alloys containing a large amount of chromium offer an interesting solution for these applications. They show a good balance between hardness and ductility in comparison to ceramics or noble metals (i.e. platinum).

Moreover, they have a high corrosion resistance at high temperature due to the formation of a protective chromia (Cr2O3) layer with low solubility in molten glass [START_REF] Manfredo | Solubility of Refractory Oxides in Soda-Lime Glass[END_REF]. In the case of commercial and waste vitrification glasses, which do not contain iron oxide (or any oxide able to form a spinel with chromia), the chromium oxide layer is in direct contact with the liquid and thus, prevents the fast active corrosion of the alloy. The dissolution rate of chromia is the key to predict the lifetime of alloys in industrial processes.

The dissolution of chromia in silica-based liquids is a complex problem of diffusion coupled with chemical reactions. Consequently, the prediction of the dissolution rate of the chromia or the identification of the parameters influencing the dissolution rate is thus difficult. A model of the dissolution of chromia in molten glasses might be a useful tool.

Since the parameters such as diffusion coefficient or chemical equilibrium are known, the prediction of the dissolution rate of the oxide is possible. Recently, Schmucker et al. [START_REF] Schmucker | Correlation between chromium physicochemical properties in silicate melts and the corrosion behavior of chromia-forming alloy[END_REF] have postulated that the dissolution of chromia is limited by the diffusion of chromium in the liquid. The parameters of the dissolution such as the diffusion coefficient of chromium in the liquid can be determined by various methods, such as square wave voltammetry [START_REF] Rüssel | Self diffusion of polyvalent ions in a soda-lime-silica glass melt[END_REF][START_REF] Clauβen | Self diffusion of polyvalent ions in a borosilicate glass melt[END_REF][START_REF] Clauβen | Diffusivities of polyvalent elements in glass melts[END_REF][START_REF] Clauβen | Self-diffusivity of polyvalent ions in silicate liquids[END_REF], molecular dynamics calculation [START_REF] Horbach | Structural and dynamical properties of sodium silicate melts: an investigation by molecular dynamics computer simulation[END_REF][START_REF] Bauchy | Viscosity and viscosity anomalies of model silicates and magmas: A numerical investigation[END_REF] or Electron Probe Micro Analysis (EPMA) [START_REF] Pablo | Multicomponent diffusion in sodium borosilicate glasses[END_REF].

Various chemical reactions of chromium in molten silicate have also been identified [START_REF] Khedim | Redox-Control Solubility of Chromium Oxide in Soda-Silicate Melts[END_REF][START_REF] Khedim | Solubility of chromium oxide in binary soda-silicate melts[END_REF] with the associated thermodynamic data.

In this paper, a model of the dissolution of chromia in simple Na2O-SiO2 liquids is proposed. Various physical phenomena such as electro-neutrality of the liquid, interface recession and mechanical equilibrium are considered in addition to the chemical diffusion and equilibria. Simple procedures are proposed in order to implement these phenomena in a mathematical model that can be easily solved. The thermodynamic data have been determined from data available in the literature. The Ni-30(wt%.)Cr alloy has been oxidized in order to form a thick chromia layer. The alloy has then been immersed in a simple Na O C. E SiO C.FE liquid at 1150 °C and the diffusion profile of chromium has been measured by EPMA at room temperature. The obtained results were compared to the simulation. Eventually, the phenomena having a significant influence on the dissolution rate of chromia are identified showing that a simplification of the model is possible when considering certain assumptions. This simplification can become the basis of a model that could be used to study the corrosion of chromia forming alloys in molten glasses and thus optimize their lifetime in industrial processes.

Materials and methods

Glass and alloy elaboration

The selected Ni-30Cr alloy was elaborated by high frequency induction melting in argon atmosphere, in order to avoid the oxidation of chromium. Ingot of 3 kg was melted from pure chromium (Alfa Aesar chromium pieces, 3 -8 mm (0.1 -0.31 in), 99.99%) and pure nickel (Alfa Aesar nickel shot, 3 -25 mm (0.1 -0.98 in), 99.95%); more details about the synthesis and the characterization of the alloy can be found in reference [START_REF] Schmucker | Oxidation of Ni-Cr alloy at intermediate oxygen pressures. I. Diffusion mechanisms through the oxide layer[END_REF]. Rods were cut from the ingot with dimensions 25 mm × 5 mm × 3 mm, polished to P1200 and ultrasonically cleaned in ethanol.

The Na O C. E SiO C.FE glass (N3S) was elaborated by the Cerfav (Centre Européen de Recherche et de Formation aux Arts Verriers) from SiO2 and Na2CO3 powders. The composition of the obtained glass was analyzed by EPMA, the results are available in reference [START_REF] Schmucker | Correlation between chromium physicochemical properties in silicate melts and the corrosion behavior of chromia-forming alloy[END_REF].

Immersion tests

The Ni-30Cr rod was sealed into a "T" shape alumina device which maintains the sample immersed in the glass contained in a Pt95Au5 (FKS) crucible (inner diameter: 30 mm, height: 30 mm). The crucible contains 15 g of glass which corresponds to 20 mm depth for immersing the sample while avoiding the contact between the alloy and the crucible and the contact between the glass and the alumina.

The sample was first oxidized in air at 1150 °C during 24 hours in order to develop a thick chromia layer (around 10 µm) on the surface of the sample [START_REF] Schmucker | Oxidation of Ni-Cr alloy at intermediate oxygen pressures. I. Diffusion mechanisms through the oxide layer[END_REF][START_REF] Schmucker | Oxidation of Ni-Cr alloy at intermediate oxygen pressures. II. Towards the lifetime prediction of alloys[END_REF]. The glass was melted and maintained at 1150 °C during 1 hour before the immersion to ensure the thermal and the chemical equilibrium of the liquid. The sample is then immersed for 1 hour. This duration is optimized to obtain a diffusion profile of chromium over several hundreds of µm while avoiding the chromium to reach the convective zone far from the interface. The sample (alloy + glass) is then quenched, removed and embedded in resin before being cut for crosssection characterizations. The section is polished with SiC grinding paper (P1200 to P4000) and diamond gel (1 µm). Immersion tests were also performed with sintered pure chromia rods but samples ended up systematically destroyed after quenching due to stresses between the chromia and the glass. The best results were obtained with the chromia-forming alloy.

EPMA characterization

The EPMA characterizations were performed with a JXA 8530F (JEOL) equipped with 5 Wavelength Dispersive X-ray Spectroscopy (WDS) analyzers. The electron beam was defocused to probe an area of 20 µm of diameter in order to integrate all the Na + ions prone to migrate out of the analyzed glass volume due to their interaction with the electron beam.

Albite (NaAlSi2O8) was used as standard for silicon and sodium and chromia was used for chromium. Oxygen was quantified using the stoichiometry of the oxide SiO2 (for Si), Na2O

(for Na) and Cr2O3 (for Cr). The analysis current was 10 nA and the analysis time was 10 seconds. The obtained result is the composition of the glass in mass fraction of SiO2, Na2O and Cr2O3.

3. Thermochemistry of the Na2O-SiO2-O2-Cr2O3 system

Acid/base properties of the Na2O-SiO2 liquid

Various models of the acid/base properties of glasses are proposed in the literature. The first description was given by Lux in 1939 [START_REF] Lux | Säuren" und "Basen" im Schmelzfluss: Die Bestimmung der Sauerstoffionen-Konzentration[END_REF]. This model links the basicity of the liquid to the quantity of "free" oxygen anion O 2-ions. The anion quantity results from the dissociation of the alkali oxides in the liquid. Based on the same idea, Toop and Somis have proposed a model in which the O 2-are in equilibrium with the bridging and the non-bridging oxygens [START_REF] Toop | Some New Ionic Concepts of Silicate Slags[END_REF]. Other approaches based on the Pauling electronegativity [START_REF] Sanderson | Electronegativities in inorganic chemistry[END_REF] or the forces of the bounds between the ions [START_REF] Sun | A scale of acidity and basicity in glass[END_REF] also exist. The optical basicity model developed by Duffy [START_REF] Duffy | A review of optical basicity and its applications to oxidic systems[END_REF] is widely used because of its simple calculation. Nevertheless, the thermodynamic approach which considers the "free" oxygen is useful to describe chemical reactions in silica-based liquids. Several measurements of this quantity (usually called the Na2O activity) using various methods have been reported in the literature. The results obtained for the Na2O-SiO2 system by transpiration technic and mass spectroscopy [START_REF] Rego | Thermodynamic study of Na2O-SiO2 melts at 1300° and 1400 °C[END_REF][START_REF] Chastel | Excess thermodynamic functions in ternary Na2O-K2O-SiO2 melts by Knudsen cell mass spectrometry[END_REF][START_REF] Zaitsev | Thermodynamics of Na2O-SiO2 melts[END_REF], electromotive force measurements [START_REF] Neudorf | Thermodynamic properties of Na2O-SiO2-CaO melts at 1000 to 1100 °C[END_REF][START_REF] Itoh | Thermodynamic activity of Na2O in Na2O-SiO2-Al2O3 melt[END_REF] and mixing enthalpy measurements [START_REF] Tsukihashi | Measurement of the Activity of Na2O in Na2O-SiO2 Melts by Chemical Equilibration Method[END_REF][START_REF] Sugawara | Thermodynamic mixing properties of liquids in the system Na2O-SiO2[END_REF] give values close to each other (from 10 -11 to 10 -5 depending on the temperature and the composition of the liquid).

The approach chosen to describe the acid/base properties of the liquid is based on chemical reactions of the silica network with Na2O. Such a model has already been presented by Maekawa et al. [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29Si MAS-NMR[END_REF]. The basic chemical reactions can be written as follow:

Q + 1 2 Na O J K ⇔ Q eq. 1 K = a N KOP a N K • a R S eq. 2
In the above equations, Q is the classical symbol to design a silica tetrahedron holding n bridging oxygens and a is the activity of the chemical species i. In the case of the Na2O-SiO2 liquids containing from 20%.mol up to 40%.mol of Na2O, the main silica tetrahedra are

Q U , Q V and Q [29,30], Q and Q C being neglectable.
The following equation can be derived from the mass balance of SiO2 and Na2O and the two mass action laws involving the three main kinds of silica tetrahedra (eq 2), the detail can be found in Appendix A.

a R = W X Y Z 9 4 λ - 3 2 λ + 1 4 _ K U -8λ -4λ K U K V + Z 3 2 λ - 1 2 _ K U 2 -4λ K U K V a b
eq. 3

In this expression, λ is the molar fraction of Na2O in the soda-silica liquid Na O SiO . The reaction constants K U and K V of the two chemical reactions (n = 4

and 3) are obtained by fitting the a R data of Sugawara et al. [START_REF] Sugawara | Thermodynamic mixing properties of liquids in the system Na2O-SiO2[END_REF] over a temperature range from 900 °C to 1500 °C and for λ ranging from 0.2 to 0.4. The fitted enthalpies and entropies of the reactions considered here are presented in table 1. The Na2O activity calculated from eq.3 and the polynomial expression proposed by Sugawara et al. are presented in figure 1.

Acid/base and redox reactions of Cr2O3 in the Na2O-SiO2 system

Solubility and redox (reduction/oxidation) properties of chromium in various glass compositions have been studied by several authors [START_REF] Schmucker | Correlation between chromium physicochemical properties in silicate melts and the corrosion behavior of chromia-forming alloy[END_REF][START_REF] Khedim | Redox-Control Solubility of Chromium Oxide in Soda-Silicate Melts[END_REF][START_REF] Khedim | Solubility of chromium oxide in binary soda-silicate melts[END_REF][START_REF] Abdullah | Dissolution equilibrium of chromium oxide in a soda lime silicate melt exposed to oxidizing and reducing atmospheres[END_REF][START_REF] Berry | The effect of composition on Cr 2+ /Cr 3+ in silicate melts[END_REF][START_REF] Kim | Enthalpies of Chromium Oxide Solution in Soda Lime Borosilicate Glass Systems[END_REF][START_REF] Roeder | Crystallization of Chromite and Chromium Solubility in Basaltic Melts[END_REF]. Three oxidation states of the chromium are possible in these media: Cr II , Cr III , Cr VI . The speciation of chromium is due to the acid/base (a R ) and the redox properties of the liquid (O2 activity in the liquid which is assumed to be in equilibrium with the O2 pressure in the atmosphere above the melt).

Khedim et al. have performed solubility measurements of chromium in the Na2O-SiO2 system for various compositions, temperatures and oxygen partial pressures [START_REF] Khedim | Solubility of chromium oxide in binary soda-silicate melts[END_REF]. They have proposed three chemical reactions (eq.4 -6):

1 2 Cr O V d e ee f ghhhhhhi Cr jjj O k V k l + m 3 2 -Xn O
eq. 4

Cr jjj O k V k l + 3 4 O + mY -X - 3 2 n O p ghhhhhi Cr qj O r r s
eq. 5

Cr jjj O k V k l t fd ghhhhhi Cr jj O u u l + 1 4 O + mX -Z - 1 2 n O
eq. 6

In these expressions, X, Y and Z are the apparent oxygen valences of Cr III , Cr VI and Cr II respectively. The O 2-activity is assimilated to the Na2O activity. The associated mass action laws are given below:

K = a vvv w xO w y • a R Z V k_ eq. 7 K = a zv { {O| O a vvv w xO w y • P V U S • a R Zr k V _ eq. 8 K = a vv } }O O • P U S • a R Zk u _
a vvv w xO w y eq. 9

In which P is the oxygen partial pressure in the atmosphere above the liquid. The activities of chromium are assimilated to the atomic fractions. The total amount of chromium in the liquid can be derived from the equations 7, 8 and 9:

x = K • a R Zk V _ m1 + K • a R Zr k V _ P V U S + K • a R Zul k_ P U S n
eq. 10

In this expression x is the total atomic fraction of chromium. Khedim et al. have evaluated the thermodynamic data independently by successive linear fits. In order to obtain more accurate values, the experimental data of solubility are fitted using directly the eq. 10.

The adjusted quantities are the three reaction enthalpies, the three reaction entropies and the three oxygen valences for the chromium. The Na O activities are calculated from the equation 3. The experimental data from Khedim et al. [START_REF] Khedim | Solubility of chromium oxide in binary soda-silicate melts[END_REF] and the values predicted by our model for the Na O C. E SiO C.FE system after the minimization of the mean square errors are presented in figure 2. The thermodynamic data are given in table 1.

Modeling the dissolution of chromia in soda-silica liquids

Chemical reactions

In the previous sections, 5 chemical reactions (two for the equation 1 and three for the equations 4, 5 and 6) have been identified. Some simplifications are possible to ease the calculation of the reaction rates. Firstly, in most of industrial applications, the atmosphere above the silica-based liquid is air or argon; the oxygen partial pressure is thus high enough to neglect the formation of Cr II (equation 6). Secondly, the Na2O or O 2-activity is extremely low in the studied range of composition (10 -10 to 10 -6 according to the previous section). The evolution of concentrations of Na2O or O 2-with time due to the chemical reactions can be relatively fast. In this case, the equations of the reaction rates shall require a thin time mesh in order to be properly integrated, thus involving a very long time of calculation to make the simulation applicable. The mass action laws can be rewritten in order to eliminate the Na2O activity from the expression without changing the equilibrium state. This can be done by substituting the Na2O activity by the Q n equilibrium (equation 2). Moreover, reaction rates are usually expressed as variations of concentration over time and concentrations are more convenient to use then molar fractions. The simplified mass action laws are rewritten to be expressed as concentration dependent, the conversions are detailed in Appendix B. They correspond to simplified reactions in which the chemical species interact directly with Q 3 and Q 4 instead of Na2O. Because these simplified reactions are obtained by substitution of Na2O by the pre-existent Q 3 /Q 4 equilibrium, the final equilibrium of the system remains the same.

H = C P

eq. 11

K " = C • K U V k • K = C vvv w xO w y • C N x V k C N ~ V k
eq. 12

K " = H V U S • K U r k V • K = C zv { {O| O • C N ~ r k V C vvv w xO w y • C V U S • C N x r k V eq. 13 K e " = K V • K U = C N • C N CN x
eq. 14

In the above expressions, K ! " is the equilibrium constant of the simplified reaction j expressed as a function of concentrations, H is the equilibrium constant (in mol.m -3 .atm -1 ) between the dissolved oxygen (O ) in the liquid and the oxygen partial pressure in the atmosphere (Henry constant), C is the concentration in mol.m -3 of the chemical species i, C is the total atomic concentration in mol.m -3 . The elimination of Na2O activity from the equilibrium leads to a new equilibrium constant K e " , which corresponds to an equilibrium between Q 4 , Q 3 and Q 2 . The reaction rates can be written as follow:

ξ = kc ZK " • C N ~ V k -C vvv w xO w y • C N x V k _ eq. 15 ξ = kc ZK " • C vvv w xO w y • C V U S • C N x r k V -C zv { {O| O • C N ~ r k V _
eq. 16

ξ e = kc e €K e " • C N x -C N • C N ~•
eq. 17

In which ξ ! is the reaction rate of the chemical reaction j (in mol.m -3 .s -1 ), kc ! is the reaction rate constant of the chemical reaction j. The thermochemical equilibrium is reached when all the chemical reaction rates are equal to zero. The variation over time of concentration of a chemical species i can be written as follows:

dC dt = ƒ v ,! ξ ! 6 ! eq. 18
In which m is the total amount of chemical reactions. The terms v ,! correspond to the stoichiometric coefficient of the compound i in the reaction j. The v ,! components can be written in a matrix form (i are the chemical compounds and j are the reactions):

…v † = ‡ ‰ 1 -1 0 0 1 0 1 2 S 0 0 0 -3 4 S 0 -3 -2X 2Y -2X -3 1 3 -2X -2Y -2X -3 -2 0 0 1 0 0 0 ‹ OE OE OE OE OE OE OE OE OE OE • ← C vvv w xO w y ← C zv { {O| O ← Cr O V ← O ← Q U ← Q V ← Q ← Na l ↑ ↑ ↑ ξ ξ ξ e
eq. 19

Mass transport

The mass transport in liquids is expressed with the Nernst-Einstein formalism. The force at the origin of the mass flow is the electrochemical gradient. A convective term is also considered. The flux of a species i is expressed as follows:

J ) * *+ = - D RT C ∇μ 0 ) ******+ + C V * *+ eq. 20
In which, J ) * *+ is the flux of the chemical species i (mol.m -2 .s -1 ), D is the diffusion coefficient, μ 0 is the electrochemical potential (J.mol -1 ), V * *+ is the velocity field of the fluid (m.s -1 ), R is the gas constant (J.mol -1 .K -1 ) and T the absolute temperature (K). The Onsager theory could be a better formalism [START_REF] Onsager | Reciprocal Relations in Irreversible Processes. I[END_REF][START_REF] Onsager | Reciprocal Relations in Irreversible Processes. II[END_REF], but the complete kinetic matrix would be complex to determine due to the large number of different chemical species. In the case of oxide layer dissolution, the above equation is defined in the reference frame in which the oxide/liquid interface is fixed in space. The unit vector is oriented from the oxide to the core of the liquid.

By developing the electrochemical potential μ 0 and assuming that the activity is equal or at least proportional to the atomic fraction (ideal or Henry approximation), the complete expression of the mass flow can be formulated as the sum of three components: Where ∇ * *+ is the classical derivative operator, z is the electric charge of the chemical species i (C.mol -1 ) and E * *+ is the electric field in the liquid. The detail of the equation 22 is

J ) * *+ = J ) '
given in Appendix C. The concentration gradients are known from the initial concentration distribution, the boundary conditions and the integration of the equation system over time, but E * *+ and V * *+ must be calculated from additional conditions.

Electric field

The electric field E * *+ is calculated in order to ensure the electro-neutrality in the liquid. In which, n is the total amount of chemical species. Thus, the following expression of the electric field can be easily derived:

E * *+ = RT ∑ z J ) '

Velocity field

The velocity field is calculated to ensure the mechanical equilibrium in the liquid. The molar volume of the liquid is postulated to be a linear combination of the molar volume of each oxide weighted by molar fraction in the liquid. A deviation of the molar volume of the liquid involves an increase of the pressure and reciprocally. The dimensionless quantity called normalized volume is defined as follows:

ν 5 = ƒ V 6 C eq. 27
In which ν 5 is the normalized volume and V 6 is the molar volume of the chemical species i (m 3 .mol -1 ). This quantity is equal to 1 when the liquid is at the mechanical equilibrium (no pressure in the liquid). The following expression corresponds to the conservation law applied to the normalized volume: The velocity field V * *+ appears in the above equation. The term τ 8 5 is the production rate of the normalized volume (s -1 ). This quantity must take into account each chemical reaction or mass flow that could lead to a variation of the normalized volume:

Boundary and initial conditions

The equations are solved over a simple finite one dimensional domain. The chromia and the liquid are in contact at the position x=0. The liquid cannot penetrate the chromia, so the flow of each chemical species across this boundary is null. At the other boundary, the concentrations are constant and equal to the initial values (at t = 0). The length of the domain remains constant during the calculation. The recession of chromia due to its dissolution is implicitly taken into account in the calculation of the velocity field.

The liquid is initially composed of Na l , O , Q U , Q V and Q . The distribution of the silica tetrahedra is given by the molar fraction of Na2O (λ), equations 2, 3 and the mass balance of silica. As an example, the liquid Na O C. E SiO C.FE at a temperature of 1150°C has a pNa2O equal to 9.08 and a distribution of silica tetrahedra corresponding to

Q U C.V˜ Q V C.Es™ Q C.CU™
; the total concentration of silicon tetrahedra being equal to the concentration of SiO2 in the liquid.

The concentration of dissolved oxygen is given by the Henry constant and the external oxygen pressure (equation 11 The presence of dissolved oxygen does not affect the distribution of silica tetrahedron. The concentration of Na2O and the total concentration of SiO2 can be easily calculated from the above equations and from the molar volume of the liquid V 6 • žf (equation 35):

V 6 • žf = χV 6 R + γV 6 š + ζV 6 eq. 35
The concentrations of Na l , O , Q U , Q V and Q at the initial time are then obvious. The liquid is also at the mechanical equilibrium as defined in section 4.2.2. (equation 27 is equal to 1).

Results

The simulations were performed with input data from tables 1 and 2 for a Na O C. E SiO C.FE liquid at 1150°C. The kinetic coefficients of the reactions have been chosen in order to quickly reach the thermochemical equilibrium. The equations system was solved using the finite volume formalism and integrated over time with a simple Euler explicit method [START_REF] Press | Numerical recipes: the art of scientific computing[END_REF]. The space mesh so as the integration time step were studied to obtain the more stable and accurate results (a relative tolerance of 10 -6 , an absolute tolerance of 10 -4 mol.m -3 and a maximum time step of 10 -4 s). The MATLAB code used to solve the equation system is available in ref [START_REF] Szczepan | Data for: A new modeling of the dissolution of chromia in Na2O-SiO2 liquids[END_REF].

The results of the simulation for 3600 seconds of reaction and the experimental results are presented in figure 3. The unknown Henry constant (H ) was adjusted to fit the solubility of the chromium, a value of 2000 mol.m -3 .atm -1 was found. This is coherent with the estimation from the literature for oxygen [START_REF] Sasabe | Permeability, diffusivity, and solubility of oxygen gas in liquid slag[END_REF] or nitrogen [START_REF] Mulfinger | Physical and Chemical Solubility of Nitrogen in Glass Melts[END_REF] in liquid slags. The simulation and the experiment are in good agreement for the diffusion of the chromium. The experimental measurements of Na2O and SiO2 concentration profiles are dispersed but consistent with the simulation.

The simulation shows an interdiffusion between the three oxides. The multi-component interdiffusion is usually attributed to cross-diffusion due to non-diagonal terms in the diffusion matrix [START_REF] Pablo | Multicomponent diffusion in sodium borosilicate glasses[END_REF][START_REF] Guo | Multicomponent diffusion in basaltic melts at 1350 °C[END_REF][START_REF] Claireaux | Influence of temperature on multicomponent diffusion in calcium and sodium aluminosilicate melts[END_REF]. In the present model, the chemical diffusion is only described by a unique diffusion coefficient and the liquid is described as an ideal mix of chemical species.

The only possible sources of interdiffusion are the velocity field (equation 30) and the migration due to the electric field (equation 26). In the Onsager formalism, each thermodynamic force can yield a mass flow [START_REF] Onsager | Reciprocal Relations in Irreversible Processes. I[END_REF][START_REF] Onsager | Reciprocal Relations in Irreversible Processes. II[END_REF] (each chemical potential gradients, the pressure gradient and the electric potential gradient). The kinetic matrix is the proportionality factor between fluxes and forces. The diffusion matrix is a simplification of the Onsager coefficients matrix when the only thermodynamic forces are the chemical potential gradients.

In the present model, the influence of the electric field and the velocity field on the diffusion can be analyzed since the equation 23 and 24 give the relation between the fluxes and these two quantities. This analysis is better detailed for chromium diffusion in section 6.3, but silicon and sodium diffusion can be stated: the electro-neutrality condition has a significant influence on the diffusion of ions with high diffusivity such as sodium and the mechanical equilibrium condition influences the diffusion of low diffusivity net-work formers such as silica. The equations 26 and 30 could be used in order to uncouple these two phenomena from the multicomponent interdiffusion in further studies.

The repartition of the Cr III , Cr VI and the dissolved oxygen are presented in figure 4. The oxygen is expressed as the external partial pressure. A decrease of the oxygen pressure towards the liquid/chromia interface can be noticed. This can be explained by the oxidation of the Cr III into Cr VI what consumes the dissolved oxygen in the liquid. The total concentration of chromium at the liquid/chromia interface is imposed by the oxygen pressure. In this simulation the oxygen pressure of 0.093 atmospheres and the total atomic fraction of chromium of 0.82 % (0.38 % Cr III and 0.44 % Cr VI ) correspond to the thermodynamic equilibrium [START_REF] Khedim | Solubility of chromium oxide in binary soda-silicate melts[END_REF].

The distribution of the Q and the resulting pNa O are presented in figure 5. The glass structure is poorly affected by the dissolution of the chromia. The pNa O exhibits a slight variation with a higher Na O activity close to the liquid/chromia interface due to the dissolution of chromia which yields "free oxygen" in the liquid and a lower Na O activity at 100 µm of the interface because of the oxidation of Cr III into Cr VI . The acid/base property of the liquid can be considered as unchanged by the dissolution of chromia. This affirmation is only verified for this specific case.

Discussion

Parabolic dissolution regime

The reaction rate constants kc , kc , kc e were chosen in order to quickly reach the chemical equilibrium in the liquid. In the present simulation, the equilibrium is reached fast enough to consider that the system is at the thermochemical equilibrium at each point of the space. As an example, the concentrations at the liquid/chromia interface evolve during 10 seconds before reaching their equilibrium values. The diffusion profiles of chromium and oxygen for various times are presented in figure 6. The concentrations remain constant at the liquid/chromia interface and the evolution of the concentrations in the liquid can be assimilated to classical diffusion profiles for semi-infinite diffusion. Thus, the dissolution rate of chromia can be described by only the solubility and the apparent diffusion coefficient of chromium in the liquid [START_REF] Schmucker | Correlation between chromium physicochemical properties in silicate melts and the corrosion behavior of chromia-forming alloy[END_REF][START_REF] Gheno | Kinetics of Al2O3-Scale Growth by Oxidation and Dissolution in Molten Silicate[END_REF][START_REF] Gheno | On the Simulation of Composition Profiles in NiCoCrAl Alloys During Al2O3 Scale Growth in Oxidation and Oxidation-Dissolution Regimes[END_REF]. The parameters influencing these two quantities are discussed in the last paragraph of this section. The dissolution rate of the oxide obeys the following parabolic law.

de dt = - V 6 x 2 S D @AA πt = - k 2t eq. 36
In this expression, e is the thickness of the oxide in m, V 6

x is the molar volume of chromia, S is the concentration of chromium at the liquid/oxide interface in mol.m -3 (i.e. solubility limit), D @AA is the apparent diffusion coefficient of the chromium in the liquid in m².s -1 and k is the parabolic dissolution constant in m².s -1 . In the presented simulation, D @AA was found to be 1 10 -12 m².s -1 (this parameter is different from the true diffusion coefficient of Cr III and Cr IV used for this calculation), S is equal to 901 mol.m -3 (0.82% atomic fraction) and the parabolic dissolution rate is 1.15 10 -16 m².s -1 . These values and the equation 36 fit the recession rate of the oxide presented in figure 7 with R² = 0.99.

Interface recession and velocity field

The problem of the moving boundary is usually encountered in materials chemistry because of the recession of an interface due to the consumption of the material. This can have a significant effect on the evolution of the considered reaction [START_REF] Wagner | Theoretical Analysis of the Diffusion Processes Determining the Oxidation Rate of Alloys[END_REF]. This aspect has not been explained in the presented model. The position x = 0 corresponds to the liquid/oxide interface in the referential in which the equations are solved. The referential can be seen as moving from the perspective of the initial referential (t = 0). This velocity is equivalent to the velocity field calculated with the equation 30. From the perspective of our referential in which the liquid/chromia interface is fixed in space, the dissolved chromia must occupy a new volume in the liquid. In order to achieve that, the liquid is pushed by the incoming matter yielding a velocity. This is encoded in the equation 30 in which this principle is generalized to the diffusion and chemical reactions.

The evolution of the velocity field at different positions and times in the liquid is presented in figure 8. By convention, the positive values correspond to a vector oriented along

x axis. The intensity of the velocity field is time dependent, but its orientation does not change. Close to the liquid/chromia interface, the velocity increases due to the diffusion of sodium and silica towards the position x = 0. The velocity converges to a time dependent value far from the interface; this value corresponds to the recession of the oxide. The velocity at the position x = 500 µm and the recession rate of the oxide are presented in figure 7; the two values are proportional. The reason of this proportionality, and not the equality, is the oxidation of chromium III in chromium VI in the liquid. Because of the higher molar volume of Cr VI set in the simulation (table 2), the dissolved chromia occupies slightly more space in the liquid than the space it occupies in the oxide layer.

Phenomena influencing the dissolution rate of chromia

Among the various phenomena highlighted in this paper, only a few seem to have a significant influence on the dissolution rate of the chromia in the silica-based liquid. The velocity field studied in the above section brings a low contribution to the diffusion of the chromium. After the 3600 seconds of simulation, the diffusion profile of chromium spreads over 200 µm while the displacement due to the velocity field is 1 µm. The electric field in the liquid is presented in figure 9; the convention for the vector field is the same as the one used for the velocity field. The value of this field is several decades of V.m -1 . The velocity of the Cr VI with its high electric charge can be calculated with the Nernst-Einstein equation. For an electric field of 50 V.m -1 the velocity of the Cr VI ion (as defined in table 2) at a temperature of 1150 °C is around 1.3 10 -10 m.s -1 , which is lower than the total velocity field. Then, both electric and velocity field have a negligible effect on the diffusion of the chromium in the liquid.

On the other hand, the oxygen pressure and diffusion in the liquid seem to have a significant influence on the dissolution rate of the chromia. As explained, the dissolution of chromia can be described by the solubility of chromium and its apparent diffusion coefficient.

The solubility of chromium depends on the acid/base properties of the liquid and the oxygen pressure at the liquid/chromia interface. The last quantity is directly related to the concentration/partial pressure of oxygen, its diffusion coefficient and the diffusion coefficients of chromium. Moreover, the evolution of the oxygen partial pressure in the liquid affects the Cr VI /Cr III ratio. It is possible to prove that the apparent diffusion coefficient of the chromium (D @AA ) can be written as follows (details in Appendix E):

D @AA = ¢P + ∂P ∂C @AA C @AA £ D vvv + ¢1 -P -∂P ∂C @AA C @AA £ D zv eq. 37

In the above expression, P is the fraction of Cr III among the total chromium concentration, noted here as C @AA . From figure 4, it can be deduced that P is slightly lower than 0.5 for this simulation. The application of equation 37 with a constant P value of 0.5 leads to a D @AA of 10 -12 m².s -1 , which is the value obtained by fitting the simulated profile of chromium with the classical erfc function or the value obtain from the dissolution rate of chromia (section 6.1.). Thus, the apparent diffusion coefficient can vary between the diffusion coefficients of Cr III and Cr VI . It appears that the model could be reduced to a system containing only Cr III , Cr VI and O2 for studying the corrosion of chromia-forming alloy in silica-based liquids.

Conclusions

A model of the dissolution of chromia in Na2O-SiO2 liquids has been developed. The aim was to formulate a model as complete as possible taking into account the physical and chemical phenomena occurring in that kind of interaction. Results from the literature were used in order to determine the thermodynamic data required for simulating the dissolution of chromia in silica-based liquids.

The equation system of the model has been solved with a numerical method. The The use of such a model for corrosion application is also debated. Since the basicity of the liquid is not affected by the dissolution of chromium, the chemical reactions can be simplified by considering a constant Na2O activity. The velocity and the electric field have a negligible effect on the dissolution of chromia. Under certain conditions, it seems that the model can be reduced to the simple diffusion of Cr III , Cr VI and O2 and the oxidation reaction of Cr III .

Figure captions

Fig. 1. Evolution of pNa2O with the composition of the binary system Na2O-SiO2 according to the data from Sugawara et al. [START_REF] Sugawara | Thermodynamic mixing properties of liquids in the system Na2O-SiO2[END_REF] (red dots) and the presented model (black lines) after minimization of the mean square errors. The term z V corresponds to the electric part (z being the electric charge and V the electric potential of the medium) and μ corresponds to the chemical part of the electrochemical potential.

Thus, the chemical diffusion is defined by the Nernst-Einstein equation as follow: The chemical potential gradient is defined by the activity. The following ratio remains constant:

χ γ = λ 1 -λ D. 3
The concentration of oxygen in the liquid is:

C = H P D. 4
The molar volume of the liquid is: The concentration of oxygen can also be written as: The equations D. 8, D. 9 and D. 10 correspond to the equations eq. 32, eq. 33 and eq. 34 respectively.

Appendix E

Equation 37

C vvv C @AA = P E. 1

The total amount of chromium corresponds to:

C @AA = C vvv + C zv E. 2
Thus, the total flux of chromium is: -D @AA dC @AA dx = -°¢P + dP dC @AA C @AA £ D vvv + ¢1 -P -dP dC @AA C @AA £ D zv ± dC @AA dx E. 7

The apparent diffusion coefficient can thus be easily identified: D @AA = ¢P + dP dC @AA C @AA £ D vvv + ¢1 -P -dP dC @AA C @AA £ D zv

E. 8

Tables Table 1. Thermodynamic data determined in this study.

Reactions ΔH (kJ.mol -1 ) ΔS (J.mol -1 .K -1 )

Q 4

Q

  silica tetrahedron holding n bridging oxygens a activity of the chemical species i K equilibrium constant between Q n , Q n-1 and Na2O. λ molar fraction of Na2O in binary Na O SiO X oxygen valence of Cr III Y oxygen valence of Cr VI Z oxygen valence of Cr II K equilibrium constant of dissolution of Cr2O3 K equilibrium constant of oxidation of Cr III in molten silicates K equilibrium constant of reduction of Cr III in molten silicates P external oxygen pressure (atm) x atomic fraction of chromium in the liquid H Henry constant of O2 (mol.m -3 .atm -1 ) C concentration of the chemical species i (mol.m -3 ) C total atomic concentration in the liquid (mol.m -3 ) K ! " equilibrium constant of the simplified reaction j expressed as a function of concentrations ξ ! reaction rate (mol.m -3 .s -1 ) kc ! kinetic constant of the reaction j v ,! stoichiometric coefficient of the compound i in the reaction j J ) * *+ flux of the chemical species i (mol.m -2 .s -1 ) D diffusion coefficient of the chemical species i (m 2 .s -1 ) R ideal gas constant (J.mol -1 .K -1 ) T temperature (K) μ 0 electro-chemical potential of the species i (J.mol -1 ) V * *+ velocity field in the liquid (m.s -1 ) z electric charge of the chemical species i (C.mol -1 ) E * *+ electric field in the liquid (V.m -1 ) production rate of the normalized volume (s -1 ) χ molar fraction of Na2O in the ternary Na O : SiO ; O < γ molar fraction of SiO2 in the ternary Na O : SiO ; O < ζ molar fraction of O2 in the ternary Na O : SiO ; O < e chromia layer thickness (m) S solubility of chromium in the liquid (mol.m -3 ) D @AA diffusion coefficient of total chromium in the liquid (m 2 .s -1 ) k parabolic dissolution constant of chromia (m 2 .s -1 ) P Cr III /Cr ratio in the liquid C @AA total Cr concentration in the liquid x distance from the liquid/oxide interface in the liquid (m) t time (s)

  t6)d *****************+ + J ) ' td )d ******************+ + J ) "td )"t ********************+

  The convective term J ) "td )"t ********************+ cannot generate space charges because the velocity is the same for all chemical species and the chemical reactions conserve intrinsically the mass and charge balances. On the other hand, the chemical flux term J ) 't6)d *****************+ can carry an electric current and thus generate space charges because of the various diffusion coefficients. The electric term J ) ' td )d *****************+ must counterbalance this electric current by satisfying the following equation: ***************+ = -ƒ z J ) 't6)d *****************+ eq. 25

  t6)d *****************+ ∑ z D C eq. 26

τ 8 5 6 !

 56 = ƒ V 6 -∇ * *+ • ZJ ) 't6)d *****************+ + J ) ' td )d ******************+ _ + ƒ v ,previous equations, i and j correspond to the chemical species and to the chemical reactions respectively. The expression for the velocity field can be obtained by imposing the time derivative of the normalized volume equal to zero in the equation 28: ∇ * *+ • V * *+ = ∑ V 6 Z∇ * *+ • ZJ ) 't6)d *****************+ + J ) ' td )d ******************+ _ + ∑ v ,The various physical and chemical phenomena developed in the previous section lead to a system of 8 partial differential equations (equation 31), one integral over space (calculation of the velocity field equation 30) and one simple relation (electric field equation 26) describing the evolution of the chemical species concentrations in the Na2O-SiO2 liquid in interaction with Cr2O3. These equations are obtained from the classical conservation law applied to the mass flows of the 8 chemical species (Cr jjj O k V k l , Cr qj O r r s , Cr O V , O , Q U , Q V , Q , Na l ) and the 3 chemical reactions (equation 15 -17): **************+ + J ) ' td )d ******************+ + J ) "td )"t ********************+ _ + ƒ v ,! ξ !

  simulation and the experimental results are in good agreement despite the dispersion of the Na2O and SiO2 measurements. The model predicts the interdiffusion of the three oxides. The electro-neutrality and mechanical equilibrium principals implemented in the model are at the origin of the interdiffusion. The model reveals that the acid/base property of the liquid is not much affected by the dissolution of the chromia. The oxidation of chromium III into chromium VI in the liquid consumes a part of the dissolved oxygen affecting the speciation and diffusion of chromium. It has been proved that the moving boundary due to the recession of the oxide during its dissolution is intrinsically considered without using re-meshing methods.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Evolution of the solubility of chromium with the oxygen fugacity in the

Fig. 4 .Fig. 5 .

 45 Fig. 4. Simulated concentration profiles of Cr III , Cr VI and O2 in Na O C. E SiO C.FE at 1150 °C after 1 hour of immersion of the pre-oxidized Ni-30Cr alloy.

Fig. 6 .

 6 Fig. 6. Simulated concentration profiles of Cr and O2 in Na O C. E SiO C.FE at 1150 °C for various immersion duration of the pre-oxidized Ni-30Cr alloy.

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. Velocity of the liquid and recession rate of chromia versus time for various distances

  **************+ = -D RT C ∇μ ) ******+ C. 2

  ***+ = ∇ Zμ ) C + RT Ln a ) _ ****************************************+ the activity is equal to the atomic fraction (ideal approximation). ***+ -C • ∇C *************+ C C. 6 Thus, the chemical potential gradient corresponds to the following expression (C. 4, C. 5 C. 6).

  C. 2 lead to the expression of the equation 22.J ) 't6)d *****************+ = -D m∇C ) ******+ -C C ∇C *************+ n

V 6

 6 §¨©ª¨« = χV 6 ¬-® + γV 6 ¯¨® + ζV 6 ® D. 5

  D. 4 and D. 6 lead to: Z1 + V 6 ® H P _ ζ = H P ZχV 6 ¬-® + γV 6 ¯¨® _ D. 7 And finally, D. 2, D. 3 and D. 7 lead to:

  Thanks to the equation E. 1 and E. 2, the equation E. 3 can be written as:

  Na O C. E SiO C.FE liquid with a Henry constant H equal to 2000 mol.m -3 .atm -1 in air (P =0.2 atm) is written as Na O C. UF SiO C.FU O C.C with data from table 2.

		ζ =	H P Z 1 -λ λ 1 -H P V 6 V 6 R	+ V 6 š _	γ	eq. 32
	γ = ›	1 1 -λ	+	χ = H P Z 1 -λ λ 1 -λ λ V 6 R γ 1 -H P V 6	+ V 6 š _ oe	eq. 33 eq. 34
	A
				). The liquid is then defined as Na O : SiO ; O < ; the relations
	between χ, γ, ζ and the known values of λ, H , P are given in equation 32, 33 and 34 (see
	Appendix D):

Table 2 .

 2 Set of parameters used in the simulation.

	1 2 Q 3 1 2 K d ⇔ Cr III O x Na 2 O Na 2 O 3 2X ⇔Q 3 K 4 K 3 ⇔Q 2 O 2 Cr 2 O 3 cristal 3 2X 1 2 Cr III O X 3 4 Y X 3 2 O 2 K o 3 2 ⇔ Cr VI O Y X O 2 2Y 6 Cr III O X 3 2X K r ⇔ Cr II O Z 2 2Z 1 4 O 2 X Z 1 2 O 2	-124.68 -112.45 80.72 -54.46 165.95	2.59 -12.52 -14.06 40.50 20.19	X = 1.36 Y = 3.22 Z = 0.64
	Chemical species ()*' + ! Cr &&& O ' 1.3 10 -12 *-). ) 0.7 10 -12 Cr ,& O -0 Cr * O ( 2.7 10 -12 O * Q / 1.0 10 -12 Q ( Q * Na + 1.0 10 -10	27020 -42460 0 -96500 -193000 96500		2.91 10 -5 3.70 10 -5 2.91 10 -5 2.46 10 -5 2.72 10 -5 1.36 10 -5
	Reaction rates
	kc 1 kc 2 kc 3		5 10 1 5 10 -1 1 10 -2

" (m².s -1 ) # " (C/mol) $ % " (m 3 .mol -1 )

Acknowledgements

The authors wish to thank the « Centre de Compétences en Microscopies, Microsondes et Métallographie » of the Jean Lamour Institute for providing the technical support for the EPMA presented in this work.

The authors also wish to thank Jean-Marc Commenge from the LRGP (Laboratoire Réaction et Génie des Procédés), Francis Kosior from the Jean Lamour institute and Gerald Monard from the LCPT (Laboratoire de Chimie et Physique Théorique) for their advice concerning numerical simulations.

Appendix A Equation 3

For a binary liquid defined as Na O SiO , the mass balances on Na2O and SiO2 are written as a function of Q n . If Q 0-1 and the free Na2O are present in low quantity, the mass balances can be written as:

With x N K the molar fraction of Q n . The equation A. 1 and A. 2 correspond respectively to the mass balance of SiO2 and Na2O. By introducing the equilibrium between Q n , Q n-1 and Na2O

(equation 1 and 2), equation A. 1 and A. 2 can be written as a function of Na2O activity (by assuming that the Q n activity and molar fraction are equivalent:

By factorization and division, one can obtain the following polynomial expression.

The Na2O activity is obtained by solving the above equation, which gives equation 3.

Appendix B

Conversion of the equilibrium constants

The aim is to convert the equilibrium constants expressed in term of activity into equilibrium constants expressed in term of concentrations and to eliminate the Na2O activity from the expressions.

The Na2O activity can be replaced by the Q 4 /Q 3 equilibrium and because of the approximation of ideal mixing, the ratio of Q n activity or concentration are equal.

The equilibrium constant K can thus be written as:

The a vvv ¤ xO w y corresponds to the atomic fraction of Cr III , K can be written as:

By keeping the concentration on one side of the equality, the new equilibrium constant K " appears obvious.

The same procedure applied to K gives.

With the Henry constant, P can be changed by the oxygen concentration.

B. 8

The constant K e " can be easily deduced by appling the same procedure to K3.

11

This procedure created a new equilibrium between Q 4 , Q 3 and Q 2 .

Appendix C Equation 22

The electrochemical potential corresponds to the following expression.


Marie M Devillers

Florence Petit

Frank Giton

Charlotte M Francois

Ludmila Juricek

Xavier Coumoul

Solange Magre

Joelle Cohen-Tannoudji

Celine J Guigon
email: celine.guigon@univ-paris-diderot.fr

Charlotte M François

Joëlle Cohen-Tannoudji

Céline J Guigon

Dr Julie Céline

Guigon

Age-dependent vulnerability of the ovary to AhR-mediated TCDD action before puberty: Evidence from mouse models

Keywords: puberty, fertility, AhR, ovary, estradiol

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

Introduction

Puberty onset and fertility are highly sensitive to environmental cues [START_REF] Tena-Sempere | Kisspeptin/GPR54 system as potential target for endocrine disruption of reproductive development and function[END_REF]. Recent epidemiological studies have pointed out the increased frequency of earlier puberty onset in girls, with possible long-term adverse outcomes on reproductive health (Aksglaede et al., 2009b(Aksglaede et al., , 2009a;;[START_REF] Euling | Role of environmental factors in the timing of puberty[END_REF]. The possible detrimental effect of endocrine disrupting chemicals (EDCs) exposure on these physiological processes has been advanced, notably because EDCs can interfere with sex hormone signaling through interaction with steroid receptors or modify steroid biosynthesis [START_REF] Parent | Current Changes in Pubertal Timing: Revised Vision in Relation with Environmental Factors Including Endocrine Disruptors[END_REF]. Timing of puberty and fertility requires estradiol (E2)-mediated maturation of neural circuitry involved in sexual cyclicity and sexual behavior during the prepubertal period [START_REF] Brock | The development of female sexual behavior requires prepubertal estradiol[END_REF][START_REF] Clarkson | Postnatal development of an estradiol-kisspeptin positive feedback mechanism implicated in puberty onset[END_REF][START_REF] Kuiri-Hänninen | Postnatal ovarian activation has effects in estrogen target tissues in infant girls[END_REF][START_REF] Stewart | Ovarian hormones act early in development to feminize adult open-field behavior in the rat[END_REF]. Analyses on rodent models have demonstrated the importance for this process of E2 synthesized at two distinct developmental stages leading to high circulating levels [START_REF] Clarkson | Effects of estradiol on kisspeptin neurons during puberty[END_REF], i.e. at the infantile stage especially during the so-called phase of mini-puberty (first two years after birth in girls, ~12-17 days postnatal [dpn] in mice) and at the late juvenile stage (~9-10 years old in girls, ~25-30 dpn in mice) [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF][START_REF] Kuiri-Hänninen | Activation of the hypothalamicpituitary-gonadal axis in infancy: minipuberty[END_REF]. A number of studies, including ours, have shown the importance of gonadotropins, i.e. luteinizing hormone (LH) and follicle-stimulating hormone (FSH), and of intra-ovarian factors for the regulation of E2 synthesis by growing follicles during the prepubertal period [START_REF] Devillers | FSH inhibits AMH to support ovarian estradiol synthesis in infantile mice[END_REF][START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF]. However, the mechanisms underlying E2 synthesis are still far from being fully elucidated. Yet, understanding how E2 synthesis is regulated during this period is of importance, notably to identify mechanisms that could impair the timing of puberty and fertility, such as those involving EDCs.

A possible pathway relaying the effects of EDCs to impair E2 synthesis in the ovary is the one regulated by the Aryl hydrocarbon receptor (AhR). Indeed, AhR is an important mediator of toxicological responses to a number of EDCs, such as 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), commonly referred to as dioxin (or the Seveso dioxin). TCDD exposure can affect E2 production, leading to altered ovulation and fertility (Li et al., 1995a(Li et al., , 1995b;;[START_REF] Salisbury | In utero and lactational exposure to 2,3,7,8tetrachlorodibenzo-p-dioxin and 2,3,4,7,8-pentachlorodibenzofuran reduces growth and disrupts reproductive parameters in female rats[END_REF]. A number of additional synthetic and natural AhR ligands, like the tryptophan metabolite carbazole), has been identified, pointing out the fact that this receptor can be activated under a large number of physiological and toxicological conditions, sometimes with different outcomes according to the nature of its ligand [START_REF] Busbee | Use of natural AhR ligands as potential therapeutic modalities against inflammatory disorders[END_REF]. In its unbound state, AhR is located in the cytoplasm and upon ligand binding, it translocates into the nucleus where it heterodimerizes with the AhR Nuclear Translocator (ARNT). The AhR/ARNT complex binds to various AhR response elements (AHRE, or XRE for xenobiotic responsive elements) depending on the nature of the ligands, to activate the expression of target genes, including that of the AhR Repressor (AhRR, encoded by the Ahrr gene), which sequesters ARNT and thereby counteracts AhR activity. It may also induce the expression of detoxifying enzymes such as Cyp1a1, enabling the metabolism of xenobiotic substances [START_REF] Guyot | The AhR twist: ligand-dependent AhR signaling and pharmaco-toxicological implications[END_REF][START_REF] Larigot | AhR signaling pathways and regulatory functions[END_REF]. In the ovary, in vivo studies on Ahr knockout mice and cell-based studies have demonstrated that intrinsic AhR signaling directly regulates the expression of cytochrome P450 19A1 aromatase (encoded by the Cyp19a1 gene), the enzyme catalyzing E2 synthesis in antral follicles using androgens as substrates, by binding to a specific XRE in the promoter of Cyp19a1 [START_REF] Baba | Intrinsic function of the aryl hydrocarbon (dioxin) receptor as a key factor in female reproduction[END_REF][START_REF] Hernandez-Ochoa | The ability of the aryl hydrocarbon receptor to regulate ovarian follicle growth and estradiol biosynthesis in mice depends on stage of sexual maturity[END_REF]. Additional works suggest that it regulates other components of the steroid biosynthesis pathway, such as steroidogenic acute regulatory protein (StAR, encoded by the Star gene), a transport protein that regulates cholesterol transfer within the mitochondria, and cytochrome P450 17A1 (encoded by the Cyp17a1 gene), an enzyme that leads to androgens biosynthesis [START_REF] Morán | Molecular target of endocrine disruption in human luteinizing granulosa cells by 2,3,7,8-tetrachlorodibenzo-p-dioxin: inhibition of estradiol secretion due to decreased 17alpha-hydroxylase/17,20-lyase cytochrome P450 expression[END_REF][START_REF] Sugawara | The effect of the arylhydrocarbon receptor on the human steroidogenic acute regulatory gene promoter activity[END_REF][START_REF] Tijet | Aryl hydrocarbon receptor regulates distinct dioxin-dependent and dioxin-independent gene batteries[END_REF]. Although intrinsic AhR signaling acts on ovarian steroidogenesis in mice around the time of puberty and in adulthood with reported differences in its effects between these two stages [START_REF] Hernandez-Ochoa | The ability of the aryl hydrocarbon receptor to regulate ovarian follicle growth and estradiol biosynthesis in mice depends on stage of sexual maturity[END_REF], there is no information regarding its physiological action on ovarian steroidogenesis during the prepubertal period.

Studies dealing with the effects of EDCs on reproductive health in humans and rodents, including ours, have mainly focused on the consequence of in utero, lactational and adult exposure [START_REF] Eskenazi | The Seveso accident: A look at 40 years of health research and beyond[END_REF][START_REF] Magre | Gender differences in transcriptional signature of developing rat testes and ovaries following embryonic exposure to 2,3,7,8-TCDD[END_REF][START_REF] Salisbury | In utero and lactational exposure to 2,3,7,8tetrachlorodibenzo-p-dioxin and 2,3,4,7,8-pentachlorodibenzofuran reduces growth and disrupts reproductive parameters in female rats[END_REF].

None has aimed at defining developmental windows of susceptibility during the prepubertal period, although the sensitivity to AhR ligands could greatly vary at this time of intensive maturation of the reproductive system. EDCs such as dioxins can enter the body upon food consumption (over 90% of contamination by dioxins) and accumulate in the adipose tissue.

Concentration of dioxins in the maternal milk (rich in lipids) is considered an important route of intake for infants, because they are very efficiently adsorbed in the digestive tracts [START_REF] Abraham | Intake and fecal excretion of PCDDs, PCDFs, HCB and PCBs (138, 153, 180) in a breast-fed and a formula-fed infant[END_REF][START_REF] Dahl | Absorption of polychlorinated biphenyls, dibenzo-p-dioxins and dibenzofurans by breast-fed infants[END_REF]. Thus, one could hypothesize that prepubertal exposure to dioxins as early as the infantile period could disrupt AhR signaling to impair ovarian steroidogenesis with possible adverse outcomes on reproductive health. On the other hand, several studies on the human population suggest an age-dependent elimination half-life of TCDD, with a markedly shorter half-life observed in infants (~5 months) as compared with that in the adults (~ 10 years), possibly related to the adipose tissue volume and rate of fecal excretion [START_REF] Kerger | Age-and concentration-dependent elimination half-life of 2,3,7,8-tetrachlorodibenzo-p-dioxin in Seveso children[END_REF][START_REF] Kreuzer | 2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) and congeners in infants. A toxicokinetic model of human lifetime body burden by TCDD with special emphasis on its uptake by nutrition[END_REF]. In view of these data, this study sought to investigate for the first time whether intrinsic AhR signaling could regulate E2 synthesis in the ovary and could be disrupted by TCDD specifically at the infantile and the late juvenile stages when its action on steroidogenesis would be critical for reproductive function programming. To address these issues, we analyzed AhR signaling at different stages of the prepubertal period in the Ahr -/-knockout mouse and in FICZ-or TCDD-treated C57BL/6 mouse harboring the Ahr b-1 allele encoding an AhR with high ligand binding affinity [START_REF] Ema | Dioxin binding activities of polymorphic forms of mouse and human arylhydrocarbon receptors[END_REF].

Methods

Animals and treatments

The colony of Ahr +/+ and Ahr -/-mice [START_REF] Fernandez-Salguero | Immune system impairment and hepatic fibrosis in mice lacking the dioxin-binding Ah receptor[END_REF] was generously provided by Dr Frank Gonzalez (NCI, National Institutes of Health, Bethesda, USA) and maintained in our animal facility. Genotyping was performed on tail genomic DNA after extraction with a buffer containing 50 mM Tris pH 8.5, 100 mM NaCl, 0.5% Tween, proteinase K 100 μg mL -1 overnight at 55 °C followed by a denaturation step at 95 °C. PCR amplification was performed with primers pairs Ahr Forward 5'-CTAGCGTGCGGGTTTCTCCT-3' and Ahr reverse 5' CAATTCTGCGCCTACACCG-3' using GoTaq Polymerase (Promega) following manufacturer's instructions. Some studies were conducted on C57BL/6JRj (Ahr b-1 ) female mice aged 14 and 28 days post-natal (dpn) or 3 months old born at the animal facility from genitors purchased at Janvier Labs (Le Genest St Isle, France). The day of birth was designed as 0 dpn. Fifty μg kg -1 of body weight (BW) of the AhR agonist, FICZ (Tocris) or vehicle (1% DMSO in saline) was subcutaneously injected twice, at both 13 and 14 dpn or at 27 and 28 dpn, and mice were then dissected 6 h after the final injection to collect ovaries. This concentration is within the usual concentration range in in vivo studies reporting a stimulatory effect of FICZ on AhR [START_REF] Jeong | FICZ, a tryptophan photoproduct, suppresses pulmonary eosinophilia and Th2-type cytokine production in a mouse model of ovalbumin-induced allergic asthma[END_REF]. FICZ is a photo by-product of tryptophan, which has high, but reversible, affinity for AhR, justifying the two injections and analyses of ovaries only 6 h after the second injection. TCDD (LGC Standards, Molsheim, France) or vehicle (0.6% nonane in corn oil) was intra-peritoneally injected at 13 dpn and 27 dpn at the dose of 5 μg kg -1 BW, and mice were dissected 24 hours later to collect ovaries and blood. We chose this dose based on our previous study showing that this concentration is followed by a significant accumulation of TCDD in adipose tissue and liver and by elevated levels in the serum, mimicking high dioxin exposure in the human population [START_REF] Duval | Chronic Exposure to Low Doses of Dioxin Promotes Liver Fibrosis Development in the C57BL/6J Diet-Induced Obesity Mouse Model[END_REF]. The number and genotypes of mice for each experiment is given in the legends of the figures. Mice were anesthetized with a mix of ketamine (Imalgene® 1000) and xylazine (Rompun® 2%) before cervical dislocation. Mice were maintained under controlled conditions (22 °C, 12 h light/dark cycle) with food (Scientific Animal Food and Engineering (SAFE), A03-10) and water available ad libitum. Experiments were performed in accordance with the ethics guidelines of the French Ministry of Agriculture and of the Ethic Committee of University of Paris (Agreement #04015.02).

Determination of intra-ovarian E2 content

The mass spectrometry coupled with gas chromatography (GC-MS) procedure was used to determine E2 content in the ovaries of Ahr +/+ and Ahr -/-mice at 14, 21 and 28 dpn or of vehicle and TCDD-treated C57BL/6 mice at 14 and 28 dpn, following a procedure described previously with some minor modifications [START_REF] Devillers | FSH inhibits AMH to support ovarian estradiol synthesis in infantile mice[END_REF]. A TQ8050 (Shimadzu, Japan) triple quadrupole mass spectrometer equipped with a chemical ionization source and operating in Q3 single ion monitoring (SIM) mode was used for detection. The linearity of E2 measurement was confirmed by plotting the ratio of the peak response/internal standard peak response to the concentration of E2 for calibration standard. Accuracy, target ions, corresponding deuterated internal control, range of detection, low limit of quantification (LLOQ), and intra & inter assay CVs of the quality control are reported in Supplemental Table 1.

FSH and LH measurements

FSH and LH were assayed using the Luminex technology with the mouse pituitary magnetic bead panel Milliplex Map kit (Merck-Millipore, Nottingham, UK), as previously described [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF].

RNA extraction, reverse transcription and quantitative real-time PCR

Pooled (2 ovaries at 7 dpn) or single ovaries (14, 21, 28 dpn and adults) were lysed with TissueLyser II (Qiagen, Courtaboeuf, France). Total RNA extraction was performed using the RNeasy mini kit (#74106, Qiagen), following manufacturers protocol as previously described [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF]. Concentration and quality of RNAs were assessed by the ratio of 260/230 nm and 260/280 nm with the Nanodrop device (Thermo Scientific, France).

Reverse transcription was performed on 100-200 ng RNA for ovaries from mice aged 7 to 14 dpn and on 1 µg for ovaries from mice aged 21 to 28 dpn using Superscript II (Invitrogen, Cergy Pontoise, France) and random primers (Invitrogen) following manufacturer's instructions. Real-time PCR was performed with Lightcycler® 480 SYBR Green I Master and Light Cycler instrument (Roche Molecular Biochemicals, La Rochelle, France). Primers used for quantitative real-time PCR were designed using Primer-BLAST (National Institutes of Health) and obtained from Eurofins (Table 1). For each primer pair, a standard curve was generated using serial dilutions of cDNA prepared from ovarian RNA and used to determine the efficiency of amplification (Cyp19a1 and Hprt amplification efficiency curves are provided in Supplementary Information). Melt-curve analysis and electrophoresis of amplified products confirmed that only a single product of the expected size was generated.

Experiments were performed from one out of the two ovaries of a female, with all samples run in triplicate reactions. Relative quantities of amplified product were calculated according to 2 -ΔΔCT method, using hypoxanthine phosphoribosyltransferase (encoded by the Hprt gene) for normalization, with the software provided by the manufacturer (Relative Quantification Software, Roche Diagnostics). Relative gene expression levels in FICZ-and TCDD-treated animals were further normalized to those of their age-matched control group.

Western blot

Ovarian protein lysates were prepared as described [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF]. Twenty µg of lysates were used for the determination of AhR (Santa-Cruz, sc-8089, dilution: 1/200) and GAPDH (Santa-Cruz, sc-25778, dilution: 1/4000). Proteins were detected by chemiluminescence with ECL using CCD camera (LAS 4000, FujiFilm). Normalization was performed by calculating the ratios of AhR to GAPDH levels after quantification of the bands with Image J software (NIH, USA, 1.64 version).

Immunohistochemistry on mouse and human ovaries

Mouse ovaries were rapidly collected and fixed for 1 hour in 4% paraformaldehyde (PFA), rinsed in PBS, dehydrated in alcohol, and paraffin-embedded using standard protocols.

Sections of 7 µm thickness were mounted on glass slides. Tissue was rehydrated and heated to 98 °C for 45 minutes in citraconic anhydride (pH 7.4) for antigen retrieval, as reported elsewhere [START_REF] Guigon | Inhibition of mTORC1 signaling reduces tumor growth but does not prevent cancer progression in a mouse model of thyroid cancer[END_REF]. Primary antibodies for AhR (Santa-Cruz, sc-8089, dilution 1/200) were incubated overnight at 4 °C. After DAB reaction (Vector), tissue sections were counterstained by hematoxylin, dehydrated and mounted in Eukitt (Sigma).

Formalin-fixed paraffin-embedded ovaries from three girls aged 2, 5 and 17 months old who died suddenly and unexpectedly, were provided by Dr Célia Ravel (INSERM U1085-IRSET, Rennes, France). The French autopsy law allows the use of such tissues for in-depth anatomopathological examination (Law 94-654, published on 29 July 1994). Autopsy was performed with informed consent of the parents in all cases. Ovaries from women of reproductive age were provided by Dr Alain Gougeon (Univ Paris, U1133, Paris, France). They were obtained from the Laboratory of Pathology of Gustave Roussy Institute (Villejuif, France) after prophylactic removal due to breast cancer between 1975 and 1980, with informed consent of the patients. These methods were carried out in accordance with relevant guidelines and regulations. All the experiments and experimental protocols on human subjects were approved by the institutional committee of the French agency for biomedical research (Agence de la Biomédecine, Saint-Denis la Plaine, France). Immunohistochemistry was performed as previously described [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF]. Slides were incubated overnight with primary antibodies for AhR (Sigma, HPA029723, dilution: 1/100). They were counterstained in hematoxylin, dehydrated and mounted in Eukitt (Sigma).

Statistical analyses

All data were analyzed by Prism 6 (version 6.0, GraphPad Software). Depending on the experimental setting, statistical analyses were performed by one-way ANOVA (one parameter and >two groups) when data showed normal distribution as assessed by the Shapiro-Wilk test, or non-parametric Kruskal-Wallis test, or using two-way ANOVA (at least two parameters) followed by Sidak's multi-comparisons tests. Data are shown as scatter dot plots with means as horizontal lines. A P value<0.05 was considered as significant.

Results

Expression of ovarian steroidogenesis-related and Ahrr genes, estradiol production and pituitary function in Ahr wild-type and knock-out mice during the prepubertal period

We first investigated whether AhR could contribute to E2 production in the ovary during the prepubertal period by analyzing AhR target genes encoding factors regulating E2 synthesis, i.e., Star, Cyp17a1 and Cyp19a1, in Ahr wild-type versus knock-out mice. For each developmental stage of the prepubertal period (depicted in Figure 1A), we selected a given age (neonatal: 7 dpn; infantile: 14 dpn; early juvenile: 21 dpn; late juvenile, when females approach puberty: 28 dpn). We started our analysis at 7 dpn, since ovarian steroidogenesis and the expression of steroidogenesis-related genes become detectable at this age in the mouse. We chose to perform this analysis on transcripts rather than on proteins due to the very small size of mouse ovaries at some studied ages. Both Ahr +/+ and Ahr -/-mice had similar expression levels of Star and Cyp17a1 at the different studied ages, except at 28 dpn when both transcripts were reduced by ~10 and ~4 fold, respectively, in Ahr -/-as compared with Ahr +/+ mice (Figures 1B andC). In addition, Ahr +/+ and Ahr -/-mice displayed similar Cyp19a1 mRNA levels at 7 and 14 dpn, and a non-significant decrease at 21 dpn (Figure 1D). However, Ahr -/-mice showed a ~3 fold reduction in Cyp19a1 relative abundance at 28 dpn, as compared with Ahr +/+ mice (Figure 1D). To further determine the impact of AhR loss on ovarian steroidogenesis, we measured the intra-ovarian content of E2 by GC-MS, which is the most accurate method to measure steroids (Figure 1E). In line with the study of gene expression, Ahr -/-mice displayed no significant changes in intra-ovarian E2 content at 14 and 21 dpn, but a significant ~5 fold decrease at 28 dpn when compared to Ahr +/+ mice. We excluded the possibility that the observed changes in ovarian steroidogenesis at 28 dpn could be related to defects in FSH synthesis and/or release by the pituitary since there was no change in circulating FSH levels at any ages (Figure 1F). It also did not result from an alteration in circulating LH levels that displayed similar levels between Ahr +/+ and Ahr -/-mice at 28 dpn. Noteworthy, circulating LH levels showed a dramatic decrease at 14 dpn in Ahr -/- mice when compared to Ahr +/+ mice (Figure 1G). We also investigated whether the observed decrease in E2 synthesis could rely on the alteration in the expression of either the FSH receptor (encoded by the Fshr gene) or the LH receptor (encoded by the Lhcgr gene), both previously reported to display reduced levels in Ahr -/-mice versus Ahr +/+ mice at puberty and in adult cycling females [START_REF] Barnett | The aryl hydrocarbon receptor is required for normal gonadotropin responsiveness in the mouse ovary[END_REF][START_REF] Hernandez-Ochoa | The ability of the aryl hydrocarbon receptor to regulate ovarian follicle growth and estradiol biosynthesis in mice depends on stage of sexual maturity[END_REF][START_REF] Teino | The aryl hydrocarbon receptor regulates mouse Fshr promoter activity through an e-box binding site[END_REF]. However, there was no alteration in the relative abundance of Fshr transcripts at 28 dpn as at any other studied age (Figures 1H andI). Lhcgr transcripts displayed no alteration in their levels at 28 dpn or at 7 and 21 dpn, but surprisingly they showed a ~2-fold decrease in their relative abundance at 14 dpn (Figures 1 I). We thus conducted subsequent experiments to determine whether Lhcgr transcript down-regulation could result from the decrease in circulating LH levels. Importantly, the pharmacological decrease in gonadotropin levels in vivo from 12 to 14 dpn led to a significant decrease in the expression of Lhcgr, while supplementation with hCG to stimulate LH signaling partially prevented this decrease (Supplementary Figure 1). Besides, treatment of cultured ovaries in serum-free medium with purified LH increased Lhcgr transcript abundance (Supplementary Figure 2).

We next sought to evaluate whether the restricted time-window of AhR action on ovarian steroidogenesis during the prepubertal period could be extended to canonical AhRregulated pathways. We analyzed in the prepubertal Ahr knockout mouse the expression of Ahrr, which is routinely used as a mark of active AhR signaling. Ahrr transcripts were detected in the ovary at all studied ages, with maximal expression levels at 14 dpn in both groups. However, there was no change in their relative abundance between the two groups at any studied ages except at 28 dpn, when Ahrr levels were ~2 fold lower in Ahr -/-mice than in Ahr +/+ mice (Figure 1J).

Effect of a putative endogenous AhR ligand, the FICZ, on ovarian steroidogenesisrelated genes, estradiol production and AhR activity at the infantile and late juvenile stages These results led us to investigate whether the lack of intrinsic AhR activity on steroidogenesis in the infantile ovary could rely on the presence of an endogenous ligand. To test this hypothesis, we used a pharmacological approach in vivo by treating infantile C57BL/6 mice with a putative endogenous ligand, the FICZ [START_REF] Rannug | Certain photooxidized derivatives of tryptophan bind with very high affinity to the Ah receptor and are likely to be endogenous signal substances[END_REF], given that ovarian ligands have not been identified yet. As a comparison, we also treated mice at the late juvenile stage, which display active AhR signaling according to our results on Ahr knockout mice, following the procedure depicted in Figure 2A.

FICZ treatment had no effect on the relative intra-ovarian abundance of Star, Cyp17a1 and Cyp19a1 at 14 dpn (Figures 2B-D). Surprisingly, it also did not affect the expression of these genes at 28 dpn, although there was a non-significant increase in the relative levels of Star and Cyp19a1 mRNA at this age (Figure 2D). In line with these findings, FICZ did not alter intra-ovarian E2 contents at either 14 or 28 dpn (Figure 2E). However, under this regimen it could efficiently stimulate AhR activity at both stages, as shown by the ~1.7 fold and ~1.4 fold increase in relative intra-ovarian Ahrr expression at 14 and 28 dpn, respectively, as compared with the control group (Figure 2F). It also dramatically upregulated the expression of the xenobiotic-metabolizing enzyme Cyp1a1 by ~7 and 10 fold at 14 and 28 dpn, respectively (Figure 2G).

TCDD-induced ovarian expression of steroidogenesis-related factors, pituitary function, and AhR activity at the infantile and late juvenile stages

We determined whether TCDD-mediated AhR action on ovarian steroidogenesis could also display a restricted time-window during the prepubertal period. To that purpose, we administered TCDD to C57BL/6 mice at either the infantile or the late juvenile stage following the same reasoning as that used for FICZ, as depicted in Figure 3A. TCDD exposure induced no alteration in Star or Cyp17a1 transcript levels at these two ages (Figures 3B,C). Importantly, it did not affect Cyp19a1 mRNA abundance at 14 dpn, but it induced an up-regulation by two-fold of Cyp19a1 mRNA abundance at 28 dpn (Figure 3D). Accordingly, TCDD treatment had no impact on intra-ovarian E2 amount at 14 dpn and it induced a ~1.5 fold increase at 28 dpn (Figure 3E). Despite documented effects of TCDD on gonadotropin expression [START_REF] Formosa | The Complex Biology of the Aryl Hydrocarbon Receptor and Its Role in the Pituitary Gland[END_REF], the measurement of circulating FSH and LH levels revealed no alteration in TCDD-treated females in comparison with vehicle-treated females at 28 dpn that could account for the observed increase in both Cyp19a1 expression and intraovarian E2 contents (Figures 3F,G). However, there was a slight but significant increase in the relative intra-ovarian abundance of Fshr transcripts that may well have impacted Cyp19a1 expression and the intra-ovarian E2 amount at this age (Figure 3H). The measurement of the relative intra-ovarian abundance of Lhcgr transcripts revealed no significant changes at 28 dpn, but a 1.3 fold decrease at 14 dpn (Figures 3I).

TCDD treatment was efficient on AhR signaling at both stages, as observed by the 2 fold up-regulation in the relative intra-ovarian Ahrr expression as compared with vehicletreated mice at 14 and 28 dpn (Figure 3J). In addition, it induced a ~20 and ~200 fold increase in the relative abundance of Cyp1a1 at 14 dpn and 28 dpn, respectively (Figure 3K).

AhR intra-ovarian levels, cellular and subcellular localization during the prepubertal period

To gain insights into the mechanisms underlying the time-restricted window of AhR action during the prepubertal period, we analyzed the intra-ovarian expression of AhR and its binding partner ARNT. We found that Ahr transcripts and proteins were present in the ovary at all studied ages during the prepubertal period (Figures 4A,B), consistent with the observation of FICZ/TCDD-mediated activation of AhR at both the infantile and late juvenile stages. No AhR protein was detected in the ovaries of Ahr -/-mice, thus confirming the specificity of the commercial antibody that we used (Figure 4B). Arnt transcripts were detected throughout the prepubertal development, being roughly stable in their relative ovarian levels between 7 and 21 dpn to subsequently decrease at 28 dpn (Figure 4C).

We next investigated by immunohistochemistry studies the cellular and subcellular

AhR expression in the ovary, with a special focus on granulosa cells, which is the cell type expressing Cyp19a1 aromatase and synthesizing E2. We used adult ovaries as positive controls, since they are known to express significant amount of AhR in the nucleus of granulosa cells of growing follicles [START_REF] Baba | Intrinsic function of the aryl hydrocarbon (dioxin) receptor as a key factor in female reproduction[END_REF][START_REF] Robles | The aryl hydrocarbon receptor, a basic helix-loop-helix transcription factor of the PAS gene family, is required for normal ovarian germ cell dynamics in the mouse[END_REF]. Our analyses of adult ovaries showed that antral follicles exhibited a notable AhR nuclear expression in virtually all granulosa cells, as expected (Figure 5Aa). A similar expression pattern could be observed in the ovaries of late juvenile females at 28 dpn harboring a prominent nuclear expression in antral follicles and in a few thecal cells (Figure 5Ab). In contrast at 14 dpn, the growing follicles located in the center of the ovary, which are responsible for E2 synthesis [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF][START_REF] Guigon | Unaltered development of the initial follicular waves and normal pubertal onset in female rats after neonatal deletion of the follicular reserve[END_REF], exhibited a faint AhR nuclear expression in a subset of granulosa cells (Figure 5Ac). Thecal cells also exhibited a weak nuclear staining. No consistent staining was observed in the ovaries of Ahr -/-mice used as controls of antibody specificity (Figure 5Ad).

We had the opportunity to evaluate AhR activity in the prepubertal human ovary, by analyzing ovaries from three infant girls aged 2, 5 and 17 months. We also used ovaries from women of reproductive age considered as positive controls. In adult human ovaries, large antral follicles displayed numerous granulosa cells with a strong nuclear expression of AhR (Figure 5Ba). By contrast, in infant ovaries, the small antral follicles, which may express CYP19A1 aromatase as described previously [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF], showed AhR expression only in a small subset of granulosa cells, with a predominant cytoplasmic expression (shown at 2 months in Figure 5Bb). A weak or low staining was observed in thecal cells and in the oocyte of these growing follicles.

Discussion

While many studies have focused on the impact of in utero or adult exposure to EDCs, few have focused on the consequence of EDC exposure from birth to puberty albeit this period may be at high risk because developmental processes are still ongoing [START_REF] Schug | Endocrine disrupting chemicals and disease susceptibility[END_REF]. In particular, E2 action would be critical during both the infantile and late juvenile stages for the proper timing of puberty, implementation of ovulation at each sexual cycle and reproductive behavior [START_REF] Clarkson | Effects of estradiol on kisspeptin neurons during puberty[END_REF]. Given the fact that AhR regulates physiological processes and can mediate EDCs action, deciphering its role on ovarian steroidogenesis during these two stages is of importance to identify the possible mechanisms whereby environmental contaminants could impair reproductive function. By using complementary approaches on the Ahr -/-mouse, treatments with FICZ or TCDD on the highly AhR sensitive C57BL/6 mouse strain and in situ analyses on mouse and human ovaries, this work provides some evidence that AhR signaling would start regulating E2 production in the ovary at the end of the prepubertal period. It highlights the existence of a time-restricted window during this period for the vulnerability of ovarian steroidogenesis to EDCs acting through AhR.

We report here that the loss of Ahr in Ahr knock-out mice led to the down-regulation in the expression of three factors involved in steroidogenesis including Star, Cyp17a1 and Cyp19a1, thereby resulting in decreased E2 synthesis by the ovary, but exclusively in late juvenile mice. Besides, administration of the prototypical AhR ligand TCDD resulted in a significant up-regulation in Fshr, Cyp19a1 expression and E2 biosynthesis in late juvenile mice and not in infantile mice. The distinct regulation of the expression of Fshr, Star and Cyp17a1 between intrinsic AhR signaling and TCDD-activated AhR signaling may reflect the occurrence of ligand-specific activation of AhR pathways, as proposed [START_REF] Guyot | The AhR twist: ligand-dependent AhR signaling and pharmaco-toxicological implications[END_REF].

This idea is further supported by our observation that TCDD, but not FICZ, could impact Cyp19a1 expression and E2 biosynthesis in late juvenile females. However, we cannot exclude that these apparent differences between FICZ and TCDD could result from the doses used for in vivo treatments and distinct kinetics of action. From the present studies, we do not know whether FICZ could be an ovarian endogenous ligand. But its relative inefficiency in regulating steroidogenesis at the late juvenile stage leads us to assume that other ligands, such as arachidonic acid, leukotrienes or heme metabolites, could mediate this process [START_REF] Guyot | The AhR twist: ligand-dependent AhR signaling and pharmaco-toxicological implications[END_REF].

Our observation that intrinsic and TCDD-mediated AhR action on ovarian steroidogenesis is related to the developmental stage parallels previous works also performed in rodents.

Indeed, regulation of intra-ovarian E2 biosynthesis by intrinsic AhR signaling was reported to be either stimulated or repressed depending on the stage of sexual maturation (30-32 dpn versus adulthood) through the use of Ahr -/-mice [START_REF] Hernandez-Ochoa | The ability of the aryl hydrocarbon receptor to regulate ovarian follicle growth and estradiol biosynthesis in mice depends on stage of sexual maturity[END_REF]. Besides, our analyses of the ovaries from rats chronically exposed in utero and through lactation to TCDD revealed no alteration in the expression of genes encoding factors involved in steroidogenesis at any studied ages from birth to the early juvenile stage [START_REF] Magre | Gender differences in transcriptional signature of developing rat testes and ovaries following embryonic exposure to 2,3,7,8-TCDD[END_REF]. Collectively, these data supports the idea that intrinsic AhR signaling, like EDC-mediated AhR activation during early prepubertal life, have no impact on E2 synthesis.

The occurrence of abnormal E2 levels despite the lack of alteration in serum FSH and LH levels in late juvenile mice with Ahr invalidation or treated with TCDD suggests that AhR signaling in the pituitary unlikely contributes to the regulation of E2 synthesis and rather supports the hypothesis of a direct implication of an ovarian AhR signaling. Besides, the observation that the levels of both Fshr and Lhcgr transcripts remained unaffected by Ahr knock-out at the late juvenile stage supports the idea that gonadotropin signaling does not interact with that of AhR to regulate E2 synthesis at this stage. The apparent discrepancy with another study led on Ahr knockout mice wherein Fshr and Lhcgr expression was downregulated as compared with that in wild-type mice, at almost the same age (30-32 dpn) may owe for distinct mouse genetic background [START_REF] Hernandez-Ochoa | The ability of the aryl hydrocarbon receptor to regulate ovarian follicle growth and estradiol biosynthesis in mice depends on stage of sexual maturity[END_REF].

We do not know at present the mechanisms underlying this stage-dependent action of intrinsic and TCDD-mediated AhR signaling on ovarian steroidogenesis during the prepubertal period. We detected AhR and the transcripts of its binding partner ARNT in the ovary at all studied prepubertal ages. The fact that FICZ and TCDD significantly induced Ahrr and Cyp1a1 in the infantile ovary indicates that the molecular machinery required for AhR transcriptional action could become functional in the ovary at an early stage, providing exogenous ligand supply. However, AhR nuclear expression was rather weak in E2synthesizing follicles in mice at the infantile stage as compared with that in adults. Although quantitative studies would be necessary to confirm these in situ data, one may hypothesize that virtually low AhR abundance in granulosa cells could be responsible for the lack of AhRmediated regulation of E2 synthesis at this stage. Importantly, our studies on human ovaries indicated that AhR expression was also virtually low in granulosa cells during infancy, therefore suggesting that the stage-dependent action of AhR occurring in the prepubertal mouse may be extended to humans. The mechanisms behind the regulation of AhR abundance have been the matter of a number of studies. The expression of AhR transcripts and proteins in granulosa cells is tightly controlled by E2 and by the gonadotropins LH and FSH [START_REF] Bussmann | Regulation of aryl hydrocarbon receptor expression in rat granulosa cells[END_REF][START_REF] Matvere | FSH/LH-Dependent Upregulation of Ahr in Murine Granulosa Cells Is Controlled by PKA Signaling and Involves Epigenetic Regulation[END_REF][START_REF] Teino | Transcriptional repression of the Ahr gene by LHCGR signaling in preovulatory granulosa cells is controlled by chromatin accessibility[END_REF]. In one of these studies, FSH and E2 were reported to decrease AhR expression in rat granulosa cells in primary culture [START_REF] Bussmann | Regulation of aryl hydrocarbon receptor expression in rat granulosa cells[END_REF], in line with the fluctuations in AhR expression during the estrus cycle in the rat [START_REF] Chaffin | Estrous cycle-dependent changes in the expression of aromatic hydrocarbon receptor (AHR) and AHR-nuclear translocator (ARNT) mRNAs in the rat ovary and liver[END_REF]. Besides, up-regulation of AhR expression in granulosa cells in vivo has been recently demonstrated to involve the cooperation of FSH and LH [START_REF] Matvere | FSH/LH-Dependent Upregulation of Ahr in Murine Granulosa Cells Is Controlled by PKA Signaling and Involves Epigenetic Regulation[END_REF]. We have shown that the growing follicles responsible for E2 synthesis at the infantile stage were responsive to FSH but not to LH, in contrast to those in late juvenile and adult ovaries [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF]. Hence, one may advance that the specific hormonal environment of the infantile period together with the low degree of maturation of growing follicles could underlie this stage-dependent action of AhR signaling in the prepubertal ovary. It would be of interest to explore this issue in future studies.

Interestingly, our analyses on Ahr wild-type and knockout mice showed that Ahr loss did not affect Ahrr expression in addition to that of steroidogenesis-related genes at the neonatal, infantile and early juvenile stages. These observations support the idea that intrinsic ovarian AhR signaling is still dormant at these early stages. The fact that Lhcgr expression was downregulated at 14 dpn may simply result from the sharp decrease in circulating LH levels at this stage, as suggested by our studies. However, the fact that TCDD could induce Ahrr and Cyp1a1 expression and represses that of Lhcgr in the infantile ovary indicates that EDCs acting through AhR could potentially impair ovarian function, aside from steroidogenesis, even at early prepubertal stages. This hypothesis is supported by our previous study carried out in the Sprague-Dawley rat exposed in utero and through lactation to TCDD [START_REF] Magre | Gender differences in transcriptional signature of developing rat testes and ovaries following embryonic exposure to 2,3,7,8-TCDD[END_REF]. These females displayed increased levels of components of the inflammatory pathway in the ovary, such as the chemokines Ccl5 (C-C motif ligand 5) and Pf4 (Platelet factor 4) at the infantile stage [START_REF] Magre | Gender differences in transcriptional signature of developing rat testes and ovaries following embryonic exposure to 2,3,7,8-TCDD[END_REF]. Chronic inflammation, as that observed in metabolic disorders related to obesity, has been linked to polycystic ovarian syndrome, altered sexual cycles and reduced oocyte quality [START_REF] Snider | Obesity Induces Ovarian Inflammation and Reduces Oocyte Quality[END_REF]. But the possibility that EDCmediated activation of AhR at early prepubertal stages could alter ovarian function to disrupt fertility warrants future studies. This is to our knowledge the first report relating that circulating LH levels are dramatically decreased in the prepubertal Ahr knockout mice, in particular at 14 dpn. We previously reported that circulating LH levels are particularly high at the time of mini-puberty in the mouse [START_REF] François | A novel action of follicle-stimulating hormone in the ovary promotes estradiol production without inducing excessive follicular growth before puberty[END_REF], but the underlying mechanisms responsible for LH surge remain unknown. LH, like FSH, is a dimeric glycoproteins composed of a common α-subunit and rate-limiting β-subunits (LHβ and FSHβ). Their synthesis and secretion is under the control of GnRH, secreted by hypothalamic neurons in a pulsatile manner. Our additional studies on gonadotropin subunits alpha (Cga), Lhbeta (Lhb) and Fshbeta (Fshb) mRNA in prepubertal Ahr +/+ and Ahr -/-mice did not reveal any alteration in their relative abundance (data not shown). Hence, the observed fall in circulating LH would not result from the loss of AhR transcriptional action on Cga or Lhb. Whether this deregulation arises from altered hypothalamic or pituitary function warrants additional studies.

In conclusion, this work highlights the existence of a window of vulnerability of ovarian steroidogenesis to AhR-mediated EDC action during the prepubertal period restricted to the late juvenile stage. It points out the existence of a developmental period at which EDCs acting via AhR could exert adverse effects on puberty onset and fertility by impacting prepubertal ovarian function. However, individuals are exposed from early life to a large number of EDCs not necessarily acting through AhR, such as Bisphenol A (BPA), which is an estrogenic Relative intra-ovarian contents of Star, Cyp17a1 and Cyp19a1 transcripts at 7, 14, 21 and 28 dpn in Ahr +/+ and Ahr -/-mice. They were determined by RT-qPCR and normalized to the mRNA levels of Hprt. The number of ovaries was the following: n=2 and 4 at 7 dpn, n=5 and 6 at 14 dpn, n=6 and 6 at 21 dpn, n=5 and 6 at 28 dpn, in Ahr +/+ and Ahr -/-mice, respectively.

(E) Intra-ovarian estradiol (E2) contents were determined by GC-MS at 14, 21 and 28 dpn in Ahr +/+ and Ahr -/-mice (n=4 to 5 mice/age group in each genotype). (F, G) Circulating FSH and LH levels were assayed by Luminex technology at 14, 21 and 28 dpn in Ahr +/+ and Ahr -/- mice (n=6 to 7 serum/age group in each genotype). (H, I, J) Relative intra-ovarian contents of Fshr, Lhcgr and Ahrr transcripts at 7, 14, 21 and 28 dpn in Ahr +/+ and Ahr -/-mice. They were determined by RT-qPCR and normalized to the mRNA levels of Hprt. The number of ovaries was the following: n=2 and 4 at 7 dpn, n=5 and 6 at 14 dpn, n=6 and 6 at 21 dpn, n=5 and 6 at 28 dpn, in Ahr +/+ and Ahr -/-mice, respectively. Data are shown as scatter dot plots with means as horizontal lines.

Figure legends Figure 1 -

 legends1 Figure legends

Figure 2 -

 2 Figure 2-FICZ-induced ovarian steroidogenesis and AhR activity in the mouse ovary at

Figure 3 -

 3 Figure 3-TCDD-induced ovarian steroidogenesis, pituitary function and AhR activity at

Figure 4

 4 Figure 4

Figure 5

 5 Figure 5

  Figure 5

  Data were analyzed by two-way ANOVA and Sidak's multi-comparisons tests with *, P<0.05; **, P<0.01; ***, P<0.001. NA, not analyzed. In (B), effect of the age P<0.05; effect of the phenotype, P>0.05; phenotype by age, P >0.05. In (C), effect of the age P<0.01; effect of the phenotype, P>0.05; phenotype by age, P>0.05. In (D), effect of the age P<0.001; effect of the phenotype, P<0.05; phenotype by age, P<0.05. In (E), effect of the age P<0.001; effect of the phenotype, P<0.01; phenotype by age, P<0.01. In (F), effect of the age P<0.001; effect of the phenotype, P>0.05; phenotype by age, P>0.05. In (G), effect of the age P<0.01; effect of the phenotype, P<0.01; phenotype by age, P<0.05. In (H), effect of the age P<0.001; effect of the phenotype, P>0.05; phenotype by age, P>0.05. In (I), effect of the age P<0.001; effect of the phenotype, P<0.05; phenotype by age, P<0.05. In (J), effect of the age P<0.001; effect of the phenotype, P>0.05; phenotype by age, P>0.05.

  Data were analyzed by two-way ANOVA and Sidak's multi-comparisons with **, P<0.01; ****, P<0.0001. In (B) and (C), effect of the age P>0.05; effect of the treatment, P>0.05; treatment by age, P>0.05. In (D), effect of the age P<0.05; effect of the treatment, P>0.05; treatment by age, P>0.05. In (E), effect of the age P<0.001; effect of the treatment, P>0.05; treatment by age, P>0.05. In (F), effect of the age P>0.05; effect of the treatment, P<0.001;

	treatment by age, P<0.05. In (G), effect of the age P>0.05; effect of the treatment, P<0.001;
	treatment by age, P>0.05.

  ****, P<0.0001. In (A), effect of the age P>0.05; effect of the treatment, P>0.05; treatment by age, P>0.05. In (B), effect of the age P>0.05; effect of the treatment, P>0.05; treatment by age, P>0.05. In (C), (F) and (G), effect of the age P<0.01, effect of the treatment, P>0.05; treatment by age, P>0.05. In (D), effect of the age P>0.05; effect of the treatment, P<0.01; treatment by age, P>0.05. In (E), effect of the age P<0.001, effect of the treatment, P<0.01; treatment by age, P<0.05. In (H) and (I), effect of the age P<0.01, effect of the treatment, P>0.05; treatment by age, P<0.05. In (J), effect of the age P>0.05; effect of the treatment, P<0.01; treatment by age, P>0.05. In (K), effect of the age P<0.01, effect of the treatment, P<0.001; treatment by age, P<0.001.

Acknowledgments

The authors thank Dr F. Gonzalez (Laboratory of Metabolism, Center of Cancer Research, National Cancer Institute, National Institutes of Health, Bethesda, MD, USA) for providing the Ahr knockout mouse strain. They acknowledge the great help of the staff from Buffon Animal Facility (Université de Paris, France). They also acknowledge the technical assistance of M. Surenaud for gonadotropin assays (IMRB-INSERM U955, Hôpital Henri Mondor, France). The authors wish to thank Dr M. Gervais for the gift of TCDD (Inserm U955-E10, Université Paris Est Créteil, France), Dr I. Ferecatu (UMR-S 1139, Université de Paris, France) for providing anti-AhR antibody, Dr A. Gougeon (Inserm U1133, Université de Paris, France) and Dr C. Ravel (INSERM U1085-IRSET, Rennes, France) for human ovarian tissue sections. They acknowledge the technical help of Mrs C. Denoyelle for her help in Western blot, Miss V. Cluzet for TCDD injections and Dr D. L'Hôte for protocol advice (Inserm U1133, Université de Paris, France). This work was supported by grants from Inserm (attributed to U1133), CNRS and Université de Paris. MMD is the recipient of a doctoral fellowship from ED BioSPC.

compound considered as a prevalent contaminant [START_REF] Vandenberg | Human exposure to bisphenol A (BPA)[END_REF]. Perinatal exposure to BPA is linked to the advent of reproductive disorders, presumably by prematurely activating E2 signaling in maturing neuronal circuitries [START_REF] Rubin | Perinatal exposure to low doses of bisphenol A affects body weight, patterns of estrous cyclicity, and plasma LH levels[END_REF][START_REF] Ruiz-Pino | Environmentally Relevant Perinatal Exposures to Bisphenol A Disrupt Postnatal Kiss1/NKB Neuronal Maturation and Puberty Onset in Female Mice[END_REF]. Future studies should determine the possible age-dependent vulnerability of the reproductive system to common EDCs during the prepubertal period.

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