Achraf El Mohajir

Jimena Castro-Gutiérrez

Rafael Luan

Sehn Canevesi

Igor Bezverkhyy

Guy Weber

Jean-Pierre Bellat

Franck Berger

Alain Celzard

Vanessa Fierro
email: vanessa.fierro@univ-lorraine.fr

Jean-Baptiste Sanchez

A Novel Porous Carbon Material for the Detection of Traces of Volatile Organic Compounds in Indoor Air

Keywords: indoor air monitoring, BTEX, miniaturized gas chromatograph, preconcentrator, hydrophobic carbon, MOF, zeolite, microporous materials

A highly sensitive and selective silicon-based micro-analytical prototype was used to identify a few ppb of volatile organic compounds (VOCs) in indoor air. Herein, a new non-activated tannin-derived carbon synthesized by an environmentally friendly method, DM2C, a MIL-101(Cr) MOF and a DaY zeolite were selected for the preconcentration of BTEX compounds (i.e. benzene, toluene, ethylbenzene and xylenes). Integrating a small amount of these nanoporous solids inside a miniaturized preconcentration unit led to excellent preconcentration performance. By taking advantage of the high adsorptiondesorption capacities of the DM2C adsorbent, concentrations as low as 23.5, 30.8, 16.7, 25 and 28.8 ppb of benzene, toluene, ethylbenzene, ortho-and para-xylene, respectively, were detected in a short analysis time ( 10 min) even in the presence of 60 % relative humidity at 25 °C. The DM2C showed excellent stability, over a period of 4 months and more than 500 tests, as well as repeatability, which makes it a very reliable adsorbent for the detection of trace VOCs in indoor air under realistic conditions in the presence of humidity.

1. INTRODUCTION BTEX compounds (i.e., benzene, toluene, ethylbenzene and xylenes) are volatile organic compounds (VOCs) that have long been known to be carcinogenic to humans even at very low concentrations, near the ppb level [START_REF] Baghani | A Case Study of BTEX Characteristics and Health Effects by Major Point Sources of Pollution during Winter in Iran[END_REF][START_REF] Bolden | New Look at BTEX: Are Ambient Levels a Problem?[END_REF][START_REF] Dehghani | Characteristics and Health Effects of BTEX in a Hot Spot for Urban Pollution[END_REF][START_REF] Masekameni | Risk Assessment of Benzene, Toluene, Ethyl Benzene, and Xylene Concentrations from the Combustion of Coal in a Controlled Laboratory Environment[END_REF]. Car exhaust, heavy industry and oil refineries are the main outdoor sources of these compounds [START_REF] Ji | A Review of Atmospheric Benzene Homologues in China: Characterization, Health Risk Assessment, Source Identification and Countermeasures[END_REF][START_REF] Truc | Roadside BTEX and Other Gaseous Air Pollutants in Relation to Emission Sources[END_REF][START_REF] Miri | Investigation of Outdoor BTEX: Concentration, Variations, Sources, Spatial Distribution, and Risk Assessment[END_REF]. On the other hand, the indoor load of these compounds is not only related to indoor activities such as smoking, cooking, heating or cleaning, but it is also partly influenced by outdoor conditions due to the penetration of ambient air pollutants into homes, especially when they are equipped with ventilation systems [START_REF] Guo | Source Characterization of BTEX in Indoor Microenvironments in Hong Kong[END_REF][START_REF] Hazrati | Preliminary Assessment of BTEX Concentrations in Indoor Air of Residential Buildings and Atmospheric Ambient Air in Ardabil, Iran[END_REF][START_REF] Demirel | Personal Exposure of Primary School Children to BTEX, NO2 and Ozone in Eskişehir, Turkey: Relationship with Indoor/Outdoor Concentrations and Risk Assessment[END_REF]. Therefore, indoor VOC levels are sometimes significantly higher than those found outdoors [START_REF] Topp | Indoor and Outdoor Air Concentrations of BTEX and NO2: Correlation of Repeated Measurements[END_REF][START_REF] Ohura | Comparative Study on Indoor Air Quality in Japan and China: Characteristics of Residential Indoor and Outdoor VOCs[END_REF]. Studies have shown that concentrations of these compounds are generally between 0.1 ppb and 50 ppb in indoor air [START_REF] Raysoni | Evaluation of VOC Concentrations in Indoor and Outdoor Microenvironments at Near-Road Schools[END_REF][START_REF] Parra | Quantification of Indoor and Outdoor Volatile Organic Compounds (VOCs) in Pubs and Cafés in Pamplona, Spain[END_REF][START_REF] Zhong | Volatile Organic Compounds (VOCs) in Conventional and High Performance School Buildings in the U[END_REF]. Therefore, in situ detection and discrimination of these VOCs in a complex mixture such as ambient air is a relevant and challenging task. Although in the last two decades a real effort has been made to develop portable and low-cost sensors for indoor air quality monitoring, methods based on gas chromatography (GC) coupled with various detectors are still the most efficient techniques employed for BTEX detection [START_REF] Dewulf | Analysis of Volatile Organic Compounds Using Gas Chromatography[END_REF][START_REF] Baimatova | Simple and Accurate Quantification of BTEX in Ambient Air by SPME and GC-MS[END_REF]. Despite their high analytical performance in terms of sensitivity and selectivity, these methods do not allow in situ analysis, mainly due to their large size, high energy and gas consumption, as well as complicated preventive maintenance. Consequently, the use of adsorbentfilled cartridges for air sampling is necessary prior to full laboratory analysis, which makes a real-time monitoring difficult [START_REF] Xu | Estimation of Indoor and Outdoor Ratios of Selected Volatile Organic Compounds in Canada[END_REF].

Our research group has developed a silicon-based microanalytical prototype, which can be considered as miniaturized gas chromatograph for a real-time analysis [START_REF] Gregis | Detection and Quantification of Lung Cancer Biomarkers by a Micro-Analytical Device Using a Single Metal Oxide-Based Gas Sensor[END_REF]. This device consists of a gas micro-preconcentrator coupled to a siliconetched spiral GC micro-column and a metal oxide-based gas sensor. Previous studies have shown that this miniaturized device allows detecting compounds in complex mixtures within minutes [START_REF] Mohsen | Development of a Micro-Analytical Prototype for Selective Trace Detection of Orthonitrotoluene[END_REF]. Preconcentration of target molecules is essential for the detection of indoor VOCs, as the levels of these pollutants are very low and mostly below the limit of detection (LOD) of various detectors. Many materials have been investigated as candidate adsorbents for the preconcentration of compounds in the gas phase [START_REF] Dettmer | Adsorbent Materials Commonly Used in Air Analysis for Adsorptive Enrichment and Thermal Desorption of Volatile Organic Compounds[END_REF][START_REF] Eyer | Methane Preconcentration by Adsorption: A Methodology for Materials and Conditions Selection[END_REF]. For this specific application and according to our previous studies, as the target gases are in very low concentration, the suitable adsorbent should have a sufficiently high adsorption affinity for VOCs, but not too high, in order to facilitate their desorption upstream the GC micro-column [START_REF] Mohsen | Selection and Characterization of Adsorbents for the Analysis of an Explosive-Related Molecule Traces in the Air[END_REF]. The adsorption-desorption process must be reversible and as fast as possible. Small pore adsorbents will be preferred because the adsorption forces are enhanced in narrow pores, provided that VOC diffusion in the porosity is not affected. In addition, as ambient air is never dry, the adsorbents must be hydrophobic in order to avoid any competitive adsorption between water and VOCs. Zeolites and activated carbon materials have been widely studied for this application due to their highly developed porous texture and good adsorption performance [START_REF] Almazán | Zeolite Based Microconcentrators for Volatile Organic Compounds Sensing at Trace-Level: Fabrication and Performance[END_REF][START_REF] Matisová | Carbon Sorbents and Their Utilization for the Preconcentration of Organic Pollutants in Environmental Samples[END_REF]. More recently, Metal Organic Frameworks (MOFs) have attracted attention as they offer many advantageous features, including high specific surface area, tailorable porosity and surface chemistry, structural diversity and interesting gas/vapor adsorption properties [START_REF] Gu | MOF-5 Metal-Organic Framework as Sorbent for In-Field Sampling and Preconcentration in Combination with Thermal Desorption GC/MS for Determination of Atmospheric Formaldehyde[END_REF][START_REF] Xie | Metal-Organic Frameworks for the Capture of Trace Aromatic Volatile Organic Compounds[END_REF][START_REF] Vellingiri | Metal Organic Frameworks as Sorption Media for Volatile and Semi-Volatile Organic Compounds at Ambient Conditions[END_REF]. These hybrid porous materials are formed by self-assembly between metal ions and organic ligands, resulting in permanent porosity [START_REF] Woellner | Adsorption and Detection of Hazardous Trace Gases by Metal-Organic Frameworks[END_REF][START_REF] Yang | Adsorption of Volatile Organic Compounds by Metal-Organic Frameworks MIL-101: Influence of Molecular Size and Shape[END_REF]. Although extensive studies have been done on the capture of harmful or toxic gases/vapors (e.g. benzene, toluene, xylene and linear hydrocarbons) by MOFs, especially MIL-101(Cr) [START_REF] Shafiei | Synthesis and Adsorption Performance of a Modified Micro-Mesoporous MIL-101(Cr) for VOCs Removal at Ambient Conditions[END_REF][START_REF] Khan | Adsorptive Removal of Hazardous Materials Using Metal-Organic Frameworks (MOFs): A Review[END_REF][START_REF] Wang | Study on the Copper(II)-Doped MIL-101(Cr) and Its Performance in VOCs Adsorption[END_REF], few researches address the preconcentration of BTEX. The use of these adsorbent materials has led to a significant breakthrough in detection limits, allowing ppb-levels to be achieved, i.e., close to those found in indoor air [START_REF] Lara-Lbeas | Sub-Ppb Level Detection of BTEX Gaseous Mixtures with a Compact Prototype GC Equipped with a Preconcentration Unit[END_REF][START_REF] Zampolli | Real-Time Monitoring of Sub-Ppb Concentrations of Aromatic Volatiles with a MEMS-Enabled Miniaturized Gas-Chromatograph[END_REF]. However, systems capable of measuring these concentrations with a relatively short analysis time are still in an early development phase and remain confined to research laboratories. The present work investigates the adsorption/desorption capacities of three types of nanoporous materials for the preconcentration and identification of BTEX in indoor air using a miniaturized analyzer. A zeolite, DaY, a MOF, MIL-101(Cr), and a non-activated, tannin-derived micromesoporous carbon, DM2C, were chosen based on their pore volume, pore size distribution and surface properties. All three of these materials have a pore diameter larger than the kinetic diameter of BTEXs and exhibit sufficiently high adsorption affinity to capture these pollutants at very low concentrations while allowing near complete desorption upon heating. After characterizing the textural properties of the selected materials, we first studied their adsorption properties in pure gas phase, for toluene and water using the thermo gravimetric technique. Then, the adsorption/desorption capacities of each adsorbent material for the preconcentration of indoor air pollutants were studied using the miniaturized analytical prototype. Specifically, a mixture of five different VOCs, i.e., benzene, toluene, ethylbenzene and ortho-/para-xylene, was selected as repre-sentative of aromatic indoor air pollutants in this study. In addition, the influence of relative humidity (RH) ranging from 2 % to 60 % at 25 °C was investigated to reproduce the indoor air environment. Here, we have demonstrated the interest of using porous solids, in particular the DM2C material, to achieve rapid detection and quantification of indoor air pollutants present even at very low concentrations. (bdc = 1,4-benzene dicarboxylate). This material was synthesized at the National Institute for Research and Development of Isotopic and Molecular Technologies (Cluj-Napoca, Romania). The synthesis is based on the reaction between CrCl 3 and H 2 bdc in a fluoride-free aqueous solution under hydrothermal conditions at 210 °C. Details of the synthesis can be found in [START_REF] Malouche | Hydrogen Absorption in 1 Nm Pd Clusters Confined in MIL-101(Cr)[END_REF].

-A hydrophobic disordered micro-mesoporous carbon prepared by a surfactant-water-assisted mechanochemical mesostructuration (SWAMM) method from mimosa tannin and referenced as DM2C in this study but originally labeled CT2P2W2_60 in [START_REF] Castro-Gutiérrez | Synthesis of Perfectly Ordered Mesoporous Carbons by Water-Assisted Mechanochemical Self-Assembly of Tannin[END_REF]. Its composition is C 7.5 O 0.6 H 0.7 . Briefly, the synthesis was carried out in a planetary ball-mill (PM 100, Retsch) where mimosa tannin, Pluronic ® F127 and water (2 g of each) were milled for 1 h, and the retrieved material was directly submitted to carbonization at 900 °C under nitrogen flow to obtain the carbon material. More details can be found elsewhere [START_REF] Castro-Gutiérrez | Synthesis of Perfectly Ordered Mesoporous Carbons by Water-Assisted Mechanochemical Self-Assembly of Tannin[END_REF]. Unlike most carbons used for the preconcentration of pollutants, DM2C did not undergo any activation step to develop its porous texture.

Characterization of the porosity of the adsorbents.

The pore textural properties of the adsorbents were characterized by Ar adsorption-desorption isotherms at -186 °C using an automatic 3-Flex adsorption device (Micromeritics) equipped with a helium cryostat to control the temperature. Before any gas adsorption, the porous solids were outgassed at 110 °C under secondary vacuum for at least 48 h. Then, Ar isotherms were measured up to the atmospheric pressure. The BET area, A BET , was calculated by applying the BET equation to the Ar adsorption branch in the adequate pressure range [START_REF] Jagiello | Carbon Slit Pore Model Incorporating Surface Energetical Heterogeneity and Geometrical Corrugation[END_REF]. The 2D non-local density functional theory for heterogeneous surfaces (2D-NLDFT HS) was applied to the Ar data in order to calculate the pore size distributions (PSDs) of the adsorbents. By integration of the PSD, we obtained the total pore volume, V T , the micropore volume, V  , and the mesopore volume, V m , was calculated as the difference between V T and V  . The PSD was also used to calculate the volume under a given pore size. 2.3. Toluene and water adsorption properties. In addition, toluene and water adsorption/desorption isotherms were measured at 25 °C by thermogravimetry (McBain type thermobalance) under controlled vapor pressure. The experimental set-up and the preparation of the organic adsorptive are described in detail in [START_REF] Bellat | Capture of Formaldehyde by Adsorption on Nanoporous Materials[END_REF]. The sample (around 15 mg) was first evacuated in situ under dynamic vacuum (10 -5 hPa) for 16 h at 400 °C for DaY and DM2C, and at 25 °C for MIL-101(Cr). Then, the sample was cooled down to 25 °C and the adsorption/desorption isotherms were measured step-by-step using a static method by introducing successively doses of toluene or water vapor into the thermobalance. Once a constant mass was reached, the next equilibrium state was performed by slightly increasing or decreasing the vapor pressure. The vapor pressure ranged from 10 -4 to about 30 hPa. 2.4. Description of the miniaturized analyzer and testing procedure. Figure 1 shows each analytical unit composing the silicon-etched micro-analytical prototype used to identify low concentrations of BTEX in indoor air. These units were connected together by silica capillaries and a six-way valve equipped with a 200 µL sampling loop [START_REF] Gregis | Detection and Quantification of Lung Cancer Biomarkers by a Micro-Analytical Device Using a Single Metal Oxide-Based Gas Sensor[END_REF]. Each selected adsorbent was deposited as a thick and homogeneous layer inside the gas micro-preconcentrators (Figures 1 (a) and 1 (b)) according to a method explained elsewhere [START_REF] Gregis | Detection and Quantification of Lung Cancer Biomarkers by a Micro-Analytical Device Using a Single Metal Oxide-Based Gas Sensor[END_REF][START_REF] Mohsen | Development of a Micro-Analytical Prototype for Selective Trace Detection of Orthonitrotoluene[END_REF]. The amount of adsorbent weighed after the deposition in each gas micro-preconcentrator was 1.2, 0.8 and 0. The testing procedure is schematized in Figure 1 (f) along with the temperature evolution over time. First, the adsorbent was exposed to a mixture of BTEX compounds at 25 °C and at a flow rate of 40 mL min -1 for 5 min (adsorption step). The BTEX compounds were generated by permeation and their initial concentrations in air were 2.35, 3.08, 1.67, 2.50 and 2.88 ppm for benzene, toluene, ethylbenzene, ortho and paraxylene, respectively. After the adsorption step, the adsorbent was heated at 170 °C for MIL-101(Cr) and 220 °C for DaY and DM2C using a PID temperature controller (heating rate  5.5 °C s -1 ), in order to desorb the concentrated VOCs towards the GC micro-column. For the MOF, the maximum desorption temperature was lower in order to avoid its thermal decomposition. After a certain time, called "desorption time", ranging from 0.25 to 2.5 min, the desorbed analytes were injected, through the injection valve, into the silicon GC micro-column heated at 35 °C. The carrier gas flow rate inside the GC microcolumn was equal to 7 mL min -1 for all experiments. The variation in the sensor response (S = (G-G°)/G°) as a function of time served as the detection signal for the system, where G is the conductance under the BTEX compounds, and G° is the conductance under carrier air flow. To compare the detection performance of the system, we plotted the evolution of the sensor response S, normalized per mg of adsorbent (S/m), as a function of time. In order to assess the presence of residual compounds desorbed from the gas micro-preconcentrator, the latter was held at the maximum desorption temperature during the separation and detection phase; then, a second injection was performed after the complete elution of all analytes from the first injection. The experiments were first conducted in nearly dry air (2 % RH at 25 °C), and then the influence of water vapor on the adsorption capacities of porous materials was also evaluated. Table 1. Composition and textural properties of the selected adsorbents.

Adsorbent Structure Formula A BET (m 2 g -1 ) V T (cm 3 g -1 ) V  (cm 3 g -1 )
V meso (cm 3 g -1 ) A BET : BET area; V T : total pore volume; V µ : micropore volume; V meso : mesopore volume approximated from the difference of V T and V µ , d m : average micropore diameter. V T , V µ , and d m were determined by application of the 2D-NLDFT-HS model.

d m (nm)
3. RESULTS AND DISCUSSION 3.1. Pore structure of the adsorbents. Figure 2 (a) shows the Ar adsorption-desorption isotherms of the selected adsorbents labeled DaY, MIL-101(Cr) and DM2C. All materials exhibit a high argon uptake at low relative pressures (p/p 0 < 0.01), confirming the existence of narrow micropores (see Figure 2 (b) for more details). DaY zeolite exhibits a small H4 hysteresis loop according to the IUPAC classification, where the adsorption branch is a combination of type I and II isotherms, associated with the presence of micropores and some mesopores [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF]. On the other hand, the DM2C isotherm exhibits an adsorption branch resulting from the combination of type I and IVa isotherms, and an H5 hysteresis loop associated with micromesoporous materials with open and partially blocked mesopores with widths above  4 nm [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF].The MIL-101(Cr) presents an isotherm derived from the combination of types I and IVb found for micro-mesoporous materials with narrow mesopores (width  4 nm) [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF]. Figure 2 (c,d) shows the differential and cumulative pore size distributions (PSDs) of the selected materials. DaY has a narrow PSD, in the micropore range, centered at  1 nm, while DM2C and MIL-101(Cr) materials feature more complex PSDs. DM2C exhibits a PSD with two distinct peaks, one in the micropore range, centered at  0.5 nm, and a second broader peak in the mesopore range at  5 nm, extending from ca. 3 to 10 nm. In contrast, MIL-101(Cr) has a PSD with two distinct broad peaks, one spanning of the micropore range from ca. 0.4 to 1.5 nm and the second centered at 2.4 nm and comprising both large micropores and narrow mesopores (width  5 nm). The textural properties of the selected adsorbents, determined from the analysis of the argon adsorption data, are reported in Table 1.

The A BET values are 382 and 762 m² g -1 for DM2C and DaY, respectively, while MIL-101(Cr) reaches an A BET of 3201 m² g - 1 and exhibits significant mesoporosity (0.92 cm 3 g -1 ), compared to the other materials. DaY has a high micropore volume, which represents more than 93 % of the total pore volume, while the micropore volume of DM2C and MIL-101(Cr) only represents 45 % and 39 % of the total pore volume, respectively. The average micropore diameter is around 0.65 nm for DM2C and slightly higher for the other materials, around 1.01 and 1.15 nm for DaY and MIL-101(Cr), respectively. Regarding the values of kinetic diameters of BTEX compounds (0.535, 0.525, 0.58, 0.68 and 0.58 nm for benzene, toluene, ethylbenzene, ortho-and para -xylene, respectively [START_REF] Li | Selective Gas Adsorption and Separation in Metal-Organic Frameworks[END_REF]) it is worth noting that all molecules can enter the pores of the selected materials. Even though the DM2C material exhibits a narrower microporosity than that observed for the DaY and MIL-101(Cr) samples (see Table 1), the wellconnected micro-mesoporosity in DM2C could increase the accessibility of the micropores [START_REF] Castro-Gutiérrez | Molecular Sieving of Linear and Branched C6 Alkanes by Tannin-Derived Carbons[END_REF], which is necessary for trapping BTEX compounds at low concentrations.

Toluene and water adsorption under equilibrium conditions.

Before evaluating the BTEX preconcentration performance of the selected adsorbents with the micro-analytical device and under dynamic conditions, toluene and water adsorption-desorption isotherms under equilibrium conditions were first measured in order to obtain more information on the adsorption capacities of these porous solids. Toluene, having an intermediate diameter, is chosen here as a representative BTEX VOC. The complete adsorption-desorption isotherms of toluene on the porous solids studied are presented in Figure 2 (e). The toluene uptake at high relative pressure (saturation plateau) can be correlated with the accessible pore volume of the solids. Given the density of liquid toluene, 0.867 g cm -3 , the amounts adsorbed at the plateau are: 1.33, 0.45 and 0.32 cm 3 g -1 for MIL-101(Cr), DM2C and DaY, respectively. The highest value was observed for MIL-101(Cr) due to the very high porosity of this material (see Table 1), in agreement with the Ar adsorption data. However, this part of the isotherm is not relevant for the present study since our goal is the preconcentration of very low concentrations of BTEX compounds (< 1 ppm or ~ 0.001 hPa or ~ p/p 0 = 2.610 -5 ). The analysis of the low-pressure part of the toluene isotherms (see insert in Figure 2 (e)) shows that the trend in this pressure range is different from that observed at saturation: the highest adsorption capacity is found for DM2C. This fact can be attributed to the well-known high adsorption affinity of carbonbased materials towards aromatic species. Comparatively, the adsorption capacity of DaY zeolite at such low pressures is much lower than those of DM2C and MIL-101(Cr). Another important characteristic of the adsorbents used for the preconcentration of BTEX compounds in ambient air is their hydrophobicity. To characterize this property, the water adsorption isotherms were measured (Figure 2 (f)). It results that DM2C and DaY are highly hydrophobic and therefore have a low water adsorption (< 0.1 g g -1 ) over a wide relative humidity range up to 60 % (water relative pressure of 0.6 at 25 °C). In contrast, MIL-101(Cr) shows a moderate water uptake up to RH ~ 35 % (p/p 0 ~ 0.35), but at higher pressure a sharp increase in the adsorbed amount is observed. This behavior suggests that in the case of MIL-101(Cr), water molecules present in the ambient air at RH above 35 % will strongly compete with BTEX species during adsorption, resulting in a less efficient preconcentration performance (see below). However, it should be kept in mind that all the results presented in this section were obtained at equilibrium from single component adsorption experiments, and that the performance of the gas micro-preconcentrator is also highly dependent on the adsorption-desorption kinetics and the gas composition.

BTEX detection performance with the microanalytical prototype.

In this section, we present results concerning the effect of the experimental conditions, in particular desorption time and relative humidity, on the detection and identification of BTEX compounds in the mixture. Figure 3 illustrates the dynamic response normalized per milligram of adsorbent (S/m), of the microsystem for the detection of a BTEX mixture with and without adsorbent in the gas micropreconcentrator for adsorption and desorption times equal to 5 and 2 min, respectively, and under nearly dry conditions (2 % RH at 25°C). These first results confirm that the device is able to selectively detect all the VOCs in the mixture in a short time,  11 min. The discrimination of each compound is attributed to the use of the GC micro-column prior to the resistive gas sensor. As expected, the response of each compound was significantly enhanced by using an adsorbent in the gas micropreconcentrator. The appearance of residual peaks after a second injection indicates that the desorption process is not complete under the conditions used. The presence of these peaks is related to the adsorption affinity of the compounds with the porous materials. Indeed, the higher the affinity, the more difficult it will be to desorb the compounds from the porous structure of the adsorbents. For all tests, an adsorption time of 5 min was applied and the concentrations of the BTEX compounds were 2.35, 3.08, 1.67, 2.50 and 2.88 ppm for benzene, toluene, ethylbenzene, orthoand para-xylene, respectively. From the normalized dynamic responses shown in Figure 3 and normalized per mg of adsorbent, these peaks are most visible for DM2C, suggesting that the adsorption affinity is the highest for this material. This result is in line with the toluene adsorption isotherm at low pressure (see insert in Figure 2 (e)). Despite this high affinity for the compounds, DM2C exhibits the best performance for the preconcentration of BTEX since the response intensity for all compounds is the highest from the first desorption cycle. As previously mentioned, the interconnected texture of DM2C favors access to the micropores, which are responsible for the surface area and therefore the BTEX adsorption capacity, compared to the other adsorbents with higher BET area and micropore volume (see Table 1). Desorption time is the key factor determining the detection performance of each compound. To be effective, the system should detect each BTEX simultaneously with the maximum possible response. Figure 4 (a) depicts the influence of desorption time on the response of each compound in dry air for the DM2C material. As can be seen in Figure 4 (a), the desorption of benzene is very fast compared to that of the other compounds in the mixture since the maximum response was obtained with a short desorption time (less than 0.5 min). With a longer desorption time, the response of benzene decreases rapidly indicating a rapid desorption from the adsorbent. The response of the other adsorbates increases gradually up to 2.5 min, except for toluene, for which starts to decrease after a desorption time equal to 1.5 min. This indicates that all of these benzene-derived compounds are more strongly adsorbed than benzene and therefore need more time to completely desorb from the adsorbents. Figure S1 demonstrates that the other materials (DaY and MIL-101(Cr)) have the same behavior. These different desorption rates of BTEX compounds can be explained by both diffusional and thermodynamic factors. The diffusion of BTEX within the porous structure of the adsorbents depends on the size of the molecule in relation to the size of the pores and their connectivity. Even though the selected VOCs exhibit similar kinetic diameters, benzene is the smallest molecule in this mixture, and hence its diffusion within the porous structure of the adsorbents is faster than that of the other compounds. On the contrary, a molecule such as ortho-xylene, exhibiting a larger kinetic diameter, will have more difficulties to enter and exit the microporosity of the adsorbents. The interaction strength of the species with the adsorbents also strongly contributes to the observed trend. Given the non-polar character of these adsorbents, the main contribution to the interactions comes from Van der Waals forces, which depend on molecular polarizabilities. Indeed, the polarizabilities of the studied species vary in the following order: o-xylene  ethylbenzene  p-xylene > toluene > benzene (see Table 2) [START_REF] Li | Selective Gas Adsorption and Separation in Metal-Organic Frameworks[END_REF]. A similar order is observed for the variation of the response of these BTEX species as a function of desorption time in our micro-analytical device (Figure 4 (a)). These different behaviors explain the disparity in desorption rate between benzene and the rest of the compounds. Thus, a compromise is needed to obtain the highest response for each compound. In nearly dry air, a desorption time equal to 2 min seems to be a good compromise to identify each chemical compound with a high response. The impact of humidity on the preconcentration performance of the system was also investigated since the relative humidity of indoor air usually varies between 30 and 60 % [START_REF] Arundel | Indirect Health Effects of Relative Humidity in Indoor Environments[END_REF]. The electrical signals presented in Figure 4 (b) show the real-time responses of the micro-system for humidity values of 30 and 60 % RH at 25°C compared to nearly dry air (2 % RH at 25 °C) after a desorption time of 2 min. It is well-known that the presence of water vapor affects the adsorption-desorption process. In the presence of humidity in the mixture, the responses of each compound decrease significantly compared to the responses in nearly dry air, for all the adsorbents used. As an example, for DM2C, the presence of humidity (60 % RH at 25 °C) in the mixture made the desorption process faster for all compounds (see Figure 4 (c)). In particular, the disparity previously noticed in dry air (see again Figure 4 (a)) was reduced and all compounds desorbed in a shorter time. The same behavior was observed for the other adsorbents (Figure S2). This can be explained by the competitive adsorption of water and BTEX on the surface of the adsorbents, occurring in multicomponent adsorption-desorption processes. Faster desorption under humid conditions allows for shorter desorption times. Thus, Figure 4 (d) displays the response of the micro-system for 30 and 60 % RH at 25 °C after reducing the desorption time to 1 min. It follows that, under humid conditions, a desorption time of 1 min leads to better results for all adsorbents compared to the optimal condition under nearly dry air (2 min desorption time). We observed that, regardless of the hydrophobic or hydrophilic nature of the selected adsorbents, the preconcentration performance was slightly reduced or, in certain cases, even improved in a humid environment. In addition, the analysis time was re- Based on these studies, DM2C appears to be a very promising adsorbent for the preconcentration of indoor air VOCs, even in the presence of high levels of relative humidity. Moreover, the efficiency of DM2C can be further increased by using longer adsorption times. Figure 5 (b) depicts the relationship between the adsorption time and the response of each compound for the DM2C material under 60 % RH at 25 °C. It is interesting to note that the response increases progressively as the adsorption time increases from 5 to 20 min, suggesting that the detection limit of the species can be lowered to a sub-ppb level. Indeed, the detection limit of the system can be extrapolated from the calibration curve as long as the sensor signal is greater than or equal to 3 times the noise (the average noise level of the gas sensor is 0.01). Finally, we performed repeatability tests as well as stability tests of the micro-system over time. Figure 5 (c) represents the evolution of the response, for each BTEX compound, obtained with the same DM2C-based gas micro-preconcentrator, in humid air (60 % RH at 25 °C) and during 18 weeks of use. It can be observed that the normalized conductance for each VOC compound shows a slight variation (between 5 % and 10 %), which may be related to the drift of the metal oxide-based gas sensor. Based on these results, over a period of 4 months and more than 500 tests that include thermal cycles, DM2C presents excellent stability and repeatability, which makes it a very reliable adsorbent for the detection of trace VOCs in indoor air under realistic relative humidity conditions. Although in the last decade, efforts have been made to develop compact detection devices [34, 44 -47], very few studies have been reported in the literature on the use of silicon-etched preconcentrator and GC micro-column units combined with a metal oxide-based gas sensor for in situ detection of BTEX in humid air. However, we can cite the work of Zampolli et al. [START_REF] Zampolli | Real-Time Monitoring of Sub-Ppb Concentrations of Aromatic Volatiles with a MEMS-Enabled Miniaturized Gas-Chromatograph[END_REF] who identified a sub-ppb benzene concentration using a sampling time of 55 min. It is noteworthy that the miniaturized prototype presented in this study allows to achieve analysis performances comparable to those presented in the literature but with shorter analysis times ( 10 min) and in humid conditions.

4. CONCLUSION In this study, we characterized the efficiency of three nanoporous solids (DaY zeolite, MIL-101(Cr) MOF and DM2C, a tannin-derived carbon) for the preconcentration of trace amounts of BTEX compounds in indoor air. Each material was placed in three different gas micro-preconcentrators that are part of a micro-analytical prototype also containing a GC micro-column and a miniaturized metal oxide-based gas sensor. With the initial BTEX mixture containing 2.35, 3.08, 1.67, 2.50 and 2.88 ppm of benzene, toluene, ethylbenzene, ortho-and para-xylene, respectively, all the selected adsorbents allowed the detection of BTEX compounds under both dry and humid conditions (up to 60 % RH at 25 °C). The response of the micro-analytical prototype to each BTEX species was evaluated as a function of desorption time and the variation was found to be molecule dependent. Due to this effect, an optimal desorption time was determined in order to detect all species. In the presence of humidity in the BTEX mixture, this desorption time was lowered to about 1 min. After diluting the initial mixture by a factor of up to 10, only the DM2C material remained efficient as preconcentration adsorbent for detecting the BTEX species. Thus, we have shown that the excellent preconcentration performance of the DM2C material allows the identification of each indoor air pollutant with concentrations as low as 23.5, 30.8, 16.7, 25 and 28.8 ppb of benzene, toluene, ethylbenzene, ortho-and para-xylene, respectively, and in a short analysis time, of approximately 10 min. DM2C also showed excellent stability and repeatability over a period of 4 months and more than 500 tests.

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website.

Pdf file including: Figure S1 showing the influence of desorption time on the response of each compound in nearly dry air for DaY and MIL-101(Cr) materials; Figure S2 that depict the influence of desorption time on the response in the presence of humidity (60 % RH at 25 °C) in the mixture for DaY and MIL-101(Cr) materials.

Figure 1 .

 1 Figure 1. (a) Silicon gas micro-preconcentrator; (b) thick layer of adsorbent: the cross-sectional SEM picture shows an example of the DM2C layer; (c) silicon gas chromatography (GC) micro-column; (d) cross-sectional SEM picture of the 100 nm PDMS stationary phase film; (e) tin oxide-based gas sensor. (f) Testing procedure: each step is schematized along with the evolution of temperature over time.

  2 mg for DaY, MIL-101(Cr) and DM2C, respectively. The inner wall of the 5-m long column (Figure1 (c)) was covered with a thin film of polydimethylsiloxane (PDMS) stationary phase (Figure1 (d)) to separate all desorbed BTEX compounds from the micropreconcentrator. Finally, a miniaturized tin oxide-based gas sensor (Figure1(e)) was used as a detector.

Figure 2 .

 2 Figure 2. Adsorptiondesorption isotherms of Ar on the DM2C carbon, DaY zeolite and MIL-101(Cr) MOF at -186 °C in (a) linear scale and (b) logarithmic scale. (c) Differential and (d) cumulative pore size distributions obtained by applying the 2D NLDFT HS model to the Ar adsorption data. (e) Toluene and (f) water adsorptiondesorption isotherms on the three selected materials at 25°C. Full symbols: adsorption; empty symbols: desorption.

Figure 3 .

 3 Figure 3. Dynamic normalized response, normalized per milligram of adsorbent, of the micro-system for the detection of BTEX in nearly dry air (2% RH at 25 °C) with and without adsorbent in the gas micro-preconcentrator (desorption time equal to 2 min).

Figure 4 .

 4 Figure 4. (a) Evolution of the response for each compound in nearly dry air (2 % RH at 25 °C) as a function of desorption time for the DM2C adsorbent. (b) Dynamic normalized response of the micro-system for the detection of BTEX as a function of humidity for each adsorbent using a desorption time of 2 min; inserts show, in more details, the dynamic responses for 30 and 60 % RH at 25 °C. (c) Evolution of the response for each compound under 60 % RH at 25 °C as a function of desorption time for the DM2C adsorbent. (d) Dynamic normalized response of the micro-system for the detection of BTEX as a function of humidity for each adsorbent using a desorption time of 1 min. For all tests, an adsorption time of 5 min was applied and the concentrations of the BTEX compounds were 2.35, 3.08, 1.67, 2.50 and 2.88 ppm for benzene, toluene, ethylbenzene, ortho-and para-xylene, respectively.

duced to  10

 10 min instead of  11 min in the case of a nearly dry atmosphere. The electrical responses to different concentrations of BTEX diluted in humid air (60 % RH at 25 °C) were also measured in order to evaluate the analytical performance of the microsystem as a function of the adsorbent used. The electrical signals presented in Figure5(a) show the real-time responses of the micro-system for different dilutions of the initial BTEX mixture (see experimental conditions) and under 60 % RH at 25 °C. As expected, the amplitude of the responses decreases with an increasing dilution ratio. For DaY and MIL-101(Cr), although benzene, toluene, ethylbenzene and para-xylene were identified, it was no longer possible to identify the presence of ortho-xylene at concentrations of 250 ppb.

Figure 5 .

 5 Figure 5. (a) Dynamic normalized response of the micro-system as a function of BTEX concentration and amplitude of the response of each VOC with an adsorption time of 5 min and a desorption time of 1 min in humid air (60 % RH at 25 °C). (b) Influence of adsorption time on the response of each VOC (1 min desorption time) for the DM2C material under 60 % RH at 25 °C. (c) Study of the repeatability and stability of the DM2C adsorbent during 18 weeks of use in humid air (60 % RH at 25 °C).

Table 2 .

 2 Comparison of polarizability () and kinetic diameter () of benzene, toluene, ethylbenzene, p-xylene, o-xylene and water[START_REF] Li | Selective Gas Adsorption and Separation in Metal-Organic Frameworks[END_REF].

	Molecule	10 3  (nm 3 )	 (nm)
	Benzene	10 -10.7	0.535
	Toluene	11.8 -12.3	0.525
	Ethylbenzene	14.2	0.580
	p-Xylene	13.7 -14.9	0.580
	o-Xylene	14.1 -14.9	0.680
	Water	1.44	0.265

Table 3 .

 3 Limit of detection (LOD) extrapolated for each compound for the DM2C adsorbent in the presence of 60 % RH at 25 °C.

	Adsorption

time (min) Benzene (ppb) Toluene (ppb) Ethylbenzene (ppb) p-Xylene (ppb) o-Xylene (ppb)

	5	12 ± 2	10 ± 1	14 ± 2	11 ± 2	21 ± 3
	10	8 ± 1.4	4 ± 0.5	8 ± 1.3	5 ± 1.1	15 ± 2
	20	4 ± 1	 1 ± 0.2	3 ± 0.7	1 ± 0.6	8 ± 1.5
	The DM2C adsorbent offers the best detection performance as
	it was still possible to identify each compound in the mixture
	with concentrations as low as 23.5, 30.8, 16.7, 25 and 28.8
	ppb of benzene, toluene, ethylbenzene, ortho-and para-xylene,
	respectively, and in the presence of humidity. It is worth not-
	ing that these concentrations are the lowest that our experi-
	mental set-up can generate (dilution of 100 from the initial
	concentrations of BTEX compounds).

  Table 3 lists the extrapolated LODs obtained for each compound. It follows that by increasing the adsorption time, we can detect all BTEX compounds present in indoor air with a high sensitivity.

ACKNOWLEDGMENT

The authors would like to express their gratitude to the Bourgogne Franche-Comté Region, the European fund FEDER and the EUR EIPHI for financial support through the project DECOLAIR. This work was partially supported by the French RENATECH network and its FEMTO-ST technological facility. FEMTO Engineering realized the silicon-etched structures (https://www.femto-engineering.fr/). The authors acknowledge Emmanuel Dordor from the Joint Mechanics Department of Femto-ST for his contribution to the design of the device. The authors from IJL also acknowledge the financial support through the TALiSMAN project, funded by ERDF (No. 2019-000214).

AUTHOR INFORMATION Corresponding Authors

* Jean-Baptiste Sanchez, Institut FEMTO-ST, UMR 6174, Université de Bourgogne -Franche-Comté, France. orcid.org/0000-0002-3303-0973; Phone: +33 3 63 08 24 93; Email: jbsanche@femto-st.fr

Author Contributions

A. El Mohajir performed the BTEX detection experiments, analyzed the data and designed the figures. J. Castro-Gutiérrez synthesized the DM2C material. R.L.S. Canevesi, V. Fierro, I. Bezverkhyy and G. Weber carried out the adsorption-desorption experiments and analyzed the data. Jean-Baptiste Sanchez conceived the presented idea, analyzed the data and took the lead in writing the manuscript. All authors contributed to the interpretation of the results, discussion and writing of the manuscript. All authors gave their approval to the final version of the manuscript.


Clément Moulin-Frier

Jean-Luc Schwartz

Julien Diard
email: julien.diard@upmf-grenoble.fr

Pierre Bessière
email: pierre.bessiere@imag.fr

Emergence of a Language through Deictic Games within a Society of Sensory-Motor Agents in Interaction

Starting from language origins theories, which connect prelinguistic primate abilities such as deixis, to modern linguistic systems, we seek to let emerge universals of human languages such as dispersion principles and the quantal aspect of speech. For this aim, we model a society of Bayesian sensory-motor agents, which interact and evolve in an environment filled with objects they can identify. We show how these agents may converge on a common phonological code for communication. This enables us to validate our assumptions and suggest probabilistic models of language origins theories.

Introduction

Since the 70's and Lindblom's proposal to "derive language from non-language", phoneticians have developed a panel of "substance-based" theories. The starting point is Lindblom's Dispersion Theory [START_REF] Liljencrants | Numerical simulation of vowel quality systems : the role of perceptual contrast[END_REF] and Stevens's Quantal Theory [START_REF] Stevens | On the quantal nature of speech[END_REF], which open the way to a rich tradition of works attempting to determine and possibly model how phonological systems could be shaped by the perceptuo-motor substance of speech communication. These works search to derive the universals of world's languages from morphologic constraints arising from perceptual (auditory and perhaps visual) and motor (articulatory and cognitive) properties: we call them "Morphogenesis Theories".

More recently, a number of proposals were introduced in order to connect pre-linguistic primate abilities (such as vocalization, gestures, mastication or deixis) to human language. In the Vocalize-to-Localize framework that we adopt in the present work [START_REF] Abry | Vocalize to localize[END_REF], human language is supposed to derive from a precursor deictic function, considering that language could have provided at the beginning an evolutionary development of the ability to "show with the voice". We call this kind of theories "Origins Theories".

We propose that the principles of Morphogenesis Theories (such as dispersion principles or the quantal nature of speech) can be incorporated and to a certain extent derived from Origins Theories. While Morphogenesis Theories ask questions such as "why are vowel systems shaped the way they are?" and answer that it is to increase auditory dispersion in order to prevent confusion between sounds, we ask questions such as "why do humans attempt to prevent confusion between percepts?" and answer that it could be to "show with the voice", that is to achieve the pre-linguistic deictic function. For this aim we model a society of bayesian agents provided with a sensory-motor apparatus and evolving in an environment filled with objects they can identify. We then describe three different behaviors describing the way in which speakers seek to produce motor gestures in front of an object and study the emergence of a common speech code as well as its properties related to Morphogenesis Theories.

Section 2 exposes the model and describes the three behaviors. Then Section 3 studies these behaviors both in a simplified and in a more realistic model of the sensory-motor apparatus. Finally Section 4 concludes and provides some perspectives.

According to the Vocalize-to-Localize framework [START_REF] Liljencrants | Numerical simulation of vowel quality systems : the role of perceptual contrast[END_REF], we model a society of agents able to produce vocalizations, perceive vocalizations and focus their joint attention on objects in their environment Thus, sensory-motor agents evolve in an environment filled with objects they can identify. Over time, they randomly meet in pairs in front of an object O. They then proceed to what we call a "deictic game", where one agent has a speaker status, and the other one has a listener status. In order to "show with the voice" this object, the speaking agent proposes a vocalization by achieving a motor gesture M. The gesture is transformed by acoustic and auditory processes into a sensory percept S, perceived by the listening agents (Figure 1). Deictic games occur in succession over time, each agent randomly taking either a speaker or a listener status. In the Bayesian Robots Programming framework [START_REF] Lebeltel | Bayesian robot programming[END_REF], agents are defined by their knowledge of a probability distribution connecting all their variables, which are, in the present study, the object O they are in front of, together with their motor state M and their perceptual state S. We consider three sub-models enabling to describe the possible behaviors of the agents. Firsly, the relation between the considered object O and the motor gesture M associated to it is called the Speaker Model. Secondly, the relation between O and the sensory percept S associated to it is called the Listener Model. Thirdly, we assume that the agents possess an internal model able to predict the sound and hence the percept that should be produced by a given motor gesture, thanks to a S=percept(M) function. This articulatory-to-acoustic efferent copy relating M and S is known to be part of the human cognitive abilities [START_REF] Frith | Neuropsychologie cognitive de la schizophrenie[END_REF], and proposed to be consistent with the mirror neuron system found in monkeys [START_REF] Iacoboni | Understanding others: imitation, language, empathy[END_REF].

If we call O S the objects in front of which agents can be in speaker status and O L the objects in front of which agents can be in listener status, the probability distribution P(O S , M, S, O S ) characterizing the behavior of the agent can be simplified, under adequate simplifications [START_REF] Moulin-Frier | Jeux déictiques dans une société d'agents sensori-moteurs[END_REF], as a product of the three sub-models:

) S | L M).P(O | ).P(S S O | P(M ) L O S, M, , S P(O ∝
This product defines the way the communication process can be implemented in each agent's knowledge state. From this state, we define three possible behaviors corresponding to different strategies of motor gesture selection in front of an object o i .

In the Reflex behavior, the speaking agent takes into consideration only its Speaker Model, by drawing a motor gesture M according to the distribution P(M| O S = o i ). In this behavior, the agent processes in a kind of reflex way just taking into account the object and not the listening process that could occur in the communication partner. We shall see that this behavior cannot lead to the emergence of a common speech code between the agents.

In the Communicative behavior, the speaking agent takes into consideration only its Listener Model, by drawing a motor gesture M in order to maximize the probability:

). percept(M) S | i o L P(O M) | i o L P(O = = = =
In this behavior, the agent thus selects a gesture providing a percept which would have allowed himself to infer the correct object. We shall see that this behavior leads to the emergence of a common phonetic code between the agents.

In the Hybrid behavior, the speaking agent takes into consideration both its Speaker and its Listener Model, by drawing a motor gesture M according to the distribution:

P(M| O S = o i , O L = o i ) = P(M| O S = o i )P(O L = o i |S=percept(M))
In this behavior, the agent takes into account both the object it perceives as a speaker, and the one it should perceive as a listener, which results in considering the product of the Reflex and Communicative behaviors. Interestingly, this incorporates the relation between production and perception in speech, where a gesture is selected both for its motor and sensory qualities.

Results

A simplified sensory-motor model

As a first step, we consider a simplified model of the sensory-motor apparatus, where M and S are simply one-dimensional bounded variables. This allows to analyze the basic properties of the three behaviors in relation with Morphogenesis Theories.

Figure 2 displays results obtained with the Reflex behavior in a society of four agents and an environment containing four objects. In a first stage, the percept function transforming motor gestures into sensory percepts is the identity function (S=M). The four upper windows represent the state of the four agents at the end of the simulation. In each window, the four Gaussian curves correspond to the distribution P(S| O L ) for each object. The lower window provides the evolution of the society with time, that is the percentage of successful games during the 1000 last ones. A game is called successful when the listener was able to correctly infer the involved object from the stimulus s provided by the speaker, using the question P(O L |S=s). It appears that the reflex behavior provides no dispersion: all Gaussian curves stay quite close to each other, indicating a lack of differentiation of gestures for different objects. In consequence, the understanding rate stays close to random (25% for four objects). 3 displays results for the Communicative behavior in the same conditions. This behavior produces a clear differentiation between gestures associated to each object, in a coherent way from one agent to another, which results in an understanding rate reaching around 80%. This recalls the "Dispersion Theory" principle introduced by Lindblom for vowels [START_REF] Liljencrants | Numerical simulation of vowel quality systems : the role of perceptual contrast[END_REF]. Actually, it can be shown that the Communicative behavior leads to a kind of maximum dispersion between means of the P(S| O L ) distributions [START_REF] Moulin-Frier | Jeux déictiques dans une société d'agents sensori-moteurs[END_REF]. Moreover, if one introduces nonlinearities in the percept function, we may simulate effects compatible with Stevens' Quantal Theory [START_REF] Stevens | On the quantal nature of speech[END_REF]. Indeed, we observe on Figure 4 that whether the nonlinearity is on the right or on the left of the motor space, the boundary between P(S| O L ) distributions for the two objects is accordingly shifted towards the right or the left. Results for the Hybrid behavior are displayed on Figure 5 in a society of four agents, an environment containing four objects and a linear percept function. As with the Communicative behavior, this behavior leads to the emergence of a common speech code between the agents, with the same properties concerning dispersion and non-linearities. It seems to be the best behavior in terms of both performance and theoretical basis. The understanding rate quickly reaches 100%. Moreover, gestures being selected both for their motor and sensory qualities, it is in line with the sensory-motor theory of speech production that we defend in our lab with the Perception for Action Control Theory (PACT, [START_REF] Schwartz | Linking the DFT and the MUAF principle in a Perception-for-Action-Control Theory (PACT)[END_REF]).

Realistic sensory-motor model

We now consider a more realistic model of the orofacial sensory-motor apparatus (VLAM, [START_REF] Boë | Modélisation de la croissance du conduit vocal. Espace vocalique des nouveaux-nés et des adultes[END_REF]) where motor gestures are three-dimensional (tongue body, tongue dorsum and lips height) and sensory percepts are two-dimensional (first formant and second effective one, in Bark). In this preliminary study, we consider static configurations corresponding to vowels. The Efference Copy Model P(S|M) is modeled by Gaussian distributions learnt through previous sensory-motor exploration. Speaker and Listener Models, P(M| O S ) and P(S| O L ) are also Gaussian distributions family, learnt during the deictic games. Figure 6 provides results for a society of two agents in a hybrid behavior and an environment containing three objects. We observe that the three vowels occupy the vertices of the vocalic triangle, that are the three vowels /a,i,u/ used in most humans languages.

Figure 1 :

 1 Figure 1: A deictic game between two agents

Figure 2 :

 2 Figure 2: Reflex behavior results in a society of four agents and an environment containing four objects

Figure

  Figure3displays results for the Communicative behavior in the same conditions. This behavior produces a clear differentiation between gestures associated to each object, in a coherent way from one agent to another, which results in an understanding rate reaching around 80%. This recalls the "Dispersion Theory" principle introduced by

Figure 3 :

 3 Figure 3: Communicative behavior results

Figure 4 :

 4 Figure 4: Upper part : two non-linear percept functions. Lower part : corresponding results in the Communicative behavior (4 agents, 2 objects).

Figure 5 :

 5 Figure 5: Hybrid behavior results

Figure 6 :

 6 Figure 6: Hybrid behavior in the vocalic triangle


V Génot
email: vincent.genot@cesr.fr

Mirror and firehose instabilities in the heliosheath

Keywords: solar wind, shock waves, plasmas, MHD, instabilities, methods: numerical

We investigate the nature of the heliosheath plasma behind the Termination Shock across which jump relations in anisotropic MHD are formulated. Along side analytical results for downstream parameters in the strictly parallel and perpendicular cases we numerically solve the Rankine-Hugoniot relations for arbitrary shock angle and strength. We then focus on two temperature anisotropy driven instabilities which have attracted attention in many other astrophysical situations, namely the mirror and firehose instabilities. It is revealed that the firehose instability is mainly controlled by the shock strength with little influence of the shock angle contrary to the mirror instability for which both parameters intervene. We confirm results showing that the heliosheath plasma observed by Voyager 1 immediately behind the Termination Shock is mirror unstable. Similar conditions are probable in the heliosheath recently encountered by Voyager 2. Finally, by comparison with studies in the Earth's magnetosheath context, we formulate predictions on the shapes of mirror associated magnetic fluctuations in the heliosheath. Both hole and peak magnetic structures were indeed observed by Voyager 1 and these shapes correspond to different stages of the mirror instability.

Introduction

Recent in-situ measurements in the heliosheath have paved the way for comparative studies with planetary magnetosheaths whose characteristics are scrutinized for many years. Among these studies the plasma turbulence induced by shocks is one of the favorite. Indeed shocks are efficient machine to produce temperature anisotropy, i.e. particle distribution functions observed downstream of shocks are anisotropic with respect to the background magnetic field. This anisotropy is a free energy which is consumed by various instabilities depending on the plasma β. Mirror mode will grow unstable in sufficiently high β plasma for T ⊥ /T > 1, whereas the firehose instability will develop for T ⊥ /T < 1 where T is the temperature and subscripts ⊥ and refer to the direction perpendicular and parallel to the ambiant magnetic field respectively. Observationally mirror associated fluctuations have been reported in different astrophysical contexts : the Earth (Génot et al. 2008a), Jupiter (Joy et al. 2006), Saturn (Bavassano Cattaneo et al. 1998), the Io wake (Huddleston et al. 1999), the comet Halley (Russell et al. 1987), the solar wind (Winterhalter et al. 1994), in front of Interplanetary Coronal Mass Ejection (Liu et al. 2006), in the heliosheath (Burlaga et al. 2006) and probably in galaxy clusters (Schekochihin et al. 2008).

On the contrary firehose associated fluctuations have been rarely reported in planetary magnetosheaths. Indeed global magnetospheric MHD simulations (Erickson et al. 2002) have shown that firehose unstable regions are very localized. Such regions are however a common feature of solar wind observations (Kasper et al. 2002) and, in the heliosheath environnement, observations of firehose instability are envisageable.

The recent in-situ measurements by Voyager 1 (V1) upstream and downstream of the Termination Shock (TS) fueled analysis which revealed that mirror instability is certainly at work in the heliosheath plasma (Burlaga et al. 2006;Liu et al. 2007). The shock crossed by V1 (hereafter TS1) was perpendicular which is implied, on average, by the tight winding of the Archimedes spiral magnetic field at large heliocentric radial distances. However other orientations may be expected especially in the downwind direction of the heliopshere where it is elongated by its interaction with the interstellar wind. Indeed recent observations by Voyager 2 (V2) (Stone et al. 2008) support the view of an asymmetric heliopshere, and the third TS crossing by V2 (hereafter TS3) is an oblique shock [START_REF] Richardson | [END_REF]. In this context, the purpose of the present paper is to propose a general procedure which addresses the question of the nature of the heliosheath plasma behind varied TS conditions characterized in term of shock angle and strength. We shall adopt an anisotropic MHD formalism keeping in mind that recent kinetic developments may be more rigorous to analyze the fine structure of the shock transition (Fahr and Siewert 2007;Siewert and Fahr 2008). In the next section we present and analytically and numerically solve the jump relations used to compute the downstream anisotropy and plasma β which are required to express instability thresholds. In Section 3 we discuss our results in the light of V1 and V2 measurements and in Section 4 predictions following an analogy with mirror mode studies in the Earth's magnetosheath context are presented.

Resolution of the jump conditions at the Termination Shock

In the following we basically follow the same approach than Liu et al. (2007). Considering a bi-Maxwellian plasma, the jump relations across a shock are Hudson (1970) :

[B n ] = 0 (1) [ρv n ] = 0 (2) [v n B t -v t B n ] = 0
(3)

P ⊥ + P -P ⊥ B 2 n B 2 + B 2 t 2µ 0 + ρv 2 n = 0 (4) B n B t µ 0 P -P ⊥ B 2 /µ 0 -1 + ρv n v t = 0 (5) ρv n 2P ⊥ ρ + P 2ρ + v 2 2 + B 2 t µ 0 ρ + B 2 n v n B 2 P -P ⊥ - ( B t • v t )B n µ 0 1 - P -P ⊥ B 2 /µ 0 = 0 (6)
The square brackets indicate the difference between pre-shock (upstream) and postshock (downstream) states, µ 0 is the permeability of the vacuum, k is the Boltzmann constant, ρ is the plasma density, v and B are the plasma velocity and magnetic field vectors respectively, P = ρkT /m is the plasma pressure, and m the proton mass; subscripts t and n denote the tangential and normal components with respect to the shock surface, and subscripts 1 and 2 in the following correspond to upstream and downstream states respectively. The velocity is measured in the shock frame and we assume that the bulk velocity is parallel to the shock normal (v t1 = 0) which is consistent with the TS being close to a spherical surface. The shock angle θ Bn is the angle between the shock normal and the Interplanetary Magnetic field at the shock, and the shock strength (or density compression ratio) r s is defined by :

r s = ρ 2 ρ 1 (7)
It can be expressed in term of normal velocities using Equation 2 and, in the case of a perpendicular shock only, is also equal to B 2 B 1 . We also define the temperature anisotropy by

A = T ⊥ /T , the upstream Alfvén Mach number M 2 A1 = µ 0 ρ 1 v 2 1 /B 2 1 and β 1 = 2µ 0 P 1 /B 2 1 .
The system of equations above is under determined (6 equations, 7 unknowns = v n2 , v t2 , B n2 , B t2 , P 2 or β 2 , A 2 , ρ 2 ) therefore solving it requires an extra information like an equation of state or a marginal stability equation (Chao et al. 1995;Vogl et al. 2001). Our approach here is different : after eliminating three quantities (v n2 , v t2 , B n2 ) we keep ρ 2 as a free parameter and compute B t2 , P 2 and A 2 as functions of r s . In the analysis of Siewert and Fahr (2008) it is shown that including CGL invariance reduces the openness of the system. Indeed the downstream anisotropy is obtained as a function of the upstream anisotropy and the shock strength only which contrasts with the MHD expressions presented below.

The system (1)-( 6) can be solved analytically in the parallel and perpendicular shock cases (Liu et al. 2007). For values of θ Bn other than 0 • and 90 • we shall use a numerical method based on a Broyden's resolution scheme [START_REF] Press | Numerical Recipes in C: the art of scientific computing[END_REF]). In the perpendicular shock case the downstream anisotropy may be expressed as

A 2 = β 1 + 2M 2 A1 1 - 1 r s + 1 -r 2 s × β 1 (5r s -4) + 2M 2 A1 r s + 3 r s -4 + 4(r s -1) -1 (8)
and in the parallel shock case :

A 2 = β 1 3 2 r s - 1 2 + M 2 A1 (1 -r s ) × β 1 (2 -r s ) + 2M 2 A1 3 -r s - 2 r s -1 (9)
For simplicity isotropic solar wind conditions are assumed (A 1 = 1). Equation 8above is equivalent to Equation 8 in Liu et al. (2007). On the contrary Equation 9 above differs from their Equation 10. We checked that solutions for downstream anisotropy computed independently 1/ from our Equation 9 and 2/ with our numerical method for θ Bn = 0 • are consistent (the anisotropy is a continuous function of θ Bn ). Accordingly the downstream anisotropy A 2 computed from our Equation 9 and displayed in the (M A1 , β 1 ) plane shows a different view from the one displayed in Figure 2 of Liu et al. (2007).

Finally, under the hypotheses of cold isotropic electrons and bi-Maxwellian plasma in the low frequency, long wavelength limit of the Vlasov-Maxwell equations, we define the mirror and firehose conditions by (Hall 1979;Hellinger 2007) :

C M = β ⊥ T ⊥ T -1 (10) C F = β 1 - T ⊥ T -1 (11)
According to these definitions the mirror and firehose instabilities occur for C M > 1 and C F > 1 respectively.

Anisotropy instabilities in the heliosheath

Our approach to determine heliosheath plasma conditions is the following. We use observations by the Voyager spacecraft and simulations to specify upstream parameters. RH relations are then solved in the (θ Bn , r s ) plane in order to determine downstream parameters and corresponding values of C M and C F . Locations of the instability thresholds are thus obtained in the (θ Bn , r s ) plane and compared to shock angle and strength effectively estimated for TS1 and TS3.

We shall discuss three types of shocks. First TS1, observed by V1 in inward motion, is considered (Liu et al. 2007); then simulated parameters for an outward motion of TS1 is studied (Whang et al. 2004). The shock parameters are distinctly different in the two situations : indeed an inward (outward) motion corresponds to periods of low (high) speed solar wind and strong (weak) shock. Finally TS3, observed by V2, is analyzed : it is a rather oblique shock contrary to TS1 which is almost perpendicular (Burlaga et al. 2008;[START_REF] Richardson | [END_REF]. Parameter values are summarized in Table 1. Four other termination shock crossings are inferred from V2 observations : TS2, observed 3.7h before TS3, is close to TS1 (outward) observed by V1 as far as parameters are concerned, TS4 is only partially observed, and TS1 (here the first crossing by V2) and TS5 occurred during telemetry gaps.

In Figure 1 isocontours of C M (solid line) and C F (dash line) are plotted in the (θ Bn , r s ) plane for TS1 in inward motion conditions (similarly in Figure 2 for TS1 in outward motion). The lines C M = 1 and C F = 1 represent the mirror and firehose instability thresholds respectively. The instability domain is below (above) this line for the mirror (firehose) instability. The contours C M = 0 and C M = 3 are discussed in the next section.

The firehose instability threshold is mostly independent of the shock angle θ Bn and obtained for stronger shocks than the mirror instability. On the contrary the influence of the shock angle is not negligible for the mirror instability whose threshold occurs for weaker shocks at large shock angles. This implies that the instability domain is larger for small θ Bn (TS classes 1, 4 and 5 as shown in Figure 1).

V1 encountered an almost perpendicular shock (θ Bn ≃ 86 • ) in inward motion (Liu et al. 2007). For these conditions the shock strength was estimated to be r s = 3.0 ± 0.2 (Whang et al. 2004) and was later inferred to be r s = 2.6 +0.4 -0.2 from the particle spectra (Stone et al. 2005). Therefore, from inspection of Figure 1 and by spanning the complete domain of strength values, the two instabilities may develop : for 2.4 < r s < 3 plasma conditions are mirror unstable (TS classes 4 and 5) whereas for 3.06 < r s < 3.2 (TS class 1) they are firehose unstable; the region 3 < r s < 3.06 is stable (TS classes 2 and 3). The situation studied in Liu et al. (2007) is showed by a cross in Figure 1 : we confirm that the plasma conditions are effectively mirror unstable (C M = 1.2). Let us note that here we use the observed angle (θ Bn = 86 • ).

On the contrary, if the shock was in outward motion, the shock strength would be smaller, in the range r s = 2.5 ± 0.2 (Whang et al. 2004). Therefore, from inspection of Figure 2, it is obvious that plasma conditions could only be mirror unstable at whatever θ Bn angles. We note that in both these situations (inward and outward motion), and for the range of parameters considered, the entropy S = 1 2 k ln(P 2 ⊥ P /ρ 5 ) increases across the shock in accordance with the second law of thermodynamics.

For upstream conditions observed ahead of TS3 (inward motion, figure not shown) the C M = 1 contour variation is similar to those shown in Figures 1 and2 and evolves from r s = 3.92 for the parallel case to r s = 3.57 for the perpendicular case. However TS3 is a very weak shock : r s ≃ 1.6 ± 0.7 [START_REF] Richardson | [END_REF], and the entropy does not increase across it according to RH relations. Indeed for these upstream conditions the shock strength should be greater than 2.88 (in the exactly perpendicular case) for the entropy to increase (smaller values apply for decreasing angles). We checked that the more extreme values given in the estimation of [START_REF] Richardson | [END_REF] (largest r s = 2.3 and smallest θ Bn = 63 • ) do not satisfy the entropy principle. One explanation may be that the particularly complex dynamics of shock reformation (actually observed by V2 (Burlaga et al. 2008)) invalidate the use of the static RH relations. Another explanation involves the computation of upstream parameters and the importance of pick-up ions. Indeed the temperature given in Table 1 for TS3 corresponds to the proton temperature only, whereas for TS1 a density-weighted average of the pick-up ion, solar wind wind proton and electron temperatures is used (Whang et al. 2004). The multi-fluid nature of the solar wind is adequately described by an effective Mach number including pick-up ion pressure (Fahr and Rucinski 1999). Similarly [START_REF] Richardson | [END_REF] explained that the heliosheath is effectively subsonic only if hot pick-up ions are considered when deriving wave properties.

Prediction on mirror associated magnetic structures

In this section we show that TS classes 3 (0 < C M < 1), 4 (1 < C M < 3) and 5 (C M > 3) may be distinguishable with respect to the shapes of mirror associated structures potentially observed behind related shocks. Indeed recent studies combining observations in the Earth's magnetosheath, hybrid (particle) simulations and theory (Soucek et al. 2008;Califano et al. 2008;Génot et al. 2008b) have shown that the shape of mirror structures are very well correlated with the distance to threshold C M . More specifically the skewness of the magnetic field amplitude distribution is negative (magnetic fluctuations look like holes) for C M < 1 and is positive (magnetic fluctuations look like peaks) for C M 2. Both kinds of structures were observed by V1 in the heliosheath (Burlaga et al. 2006). Sinusoidal or 'mixed' structures (vanishing skewness) are observed around C M ≃ 1.5. It is interesting to note that holes structures are mostly observed for mirror stable conditions. This peculiar behaviour is inherent to a bistable phenomenon (Passot et al. 2006) which allows magnetic holes to survive stable conditions whereas magnetic peaks are damped. If we transpose these results to our TS classification, we could expect to observe magnetic holes behind TS class 3. These holes would have grown from mirror unstable conditions in a separate region and would have been convected back close to the TS where they could survive according to the bistability phenomenon. Behind TS classes 4 and 5 sinusoidal mirror structures and peaks are expected with a predilection for peaks in class 5. Recent observations of multiple shock crossings with V2 may validate this scenario which would illustrate the generality of astrophysical processes such as temperature anisotropy driven instabilities.

In planetary magnetosheaths it has been shown that the plasma β decreases from the shock to the magnetopause and is anti-correlated with the anisotropy (Fuselier et al. 1994), the plasma state remaining close to the mirror marginal stability. However in the heliosheath no similar trend has yet been detected. Conditions are probably much different in the upwind and downwind directions.

Summary

This paper presents a generic procedure to infer heliosheath plasma conditions with respect to temperature anisotropy instabilities downstream of the Termination Shock for arbitrary upstream parameters, shock angle and strength. We confront this both analytical and numerical approach with in-situ measurements recorded by the Voyager spacecraft. Different types of shocks have been crossed and heliosheath plasma behind these shocks may be stable or not with respect to the mirror and firehose instabilities. The procedure proposed here allows to take into account the measurement uncertainties of the shock angle and strength in order to determine the actual downstream plasma state. The present calculation is also used to predict possible future observations in the heliosheath by comparison with the much covered Earth's bow shock and magnetosheath regions. Liu et al. (2007) for TS1 (inward), from Whang et al. (2004) for TS1 (outward) and from [START_REF] Richardson | [END_REF] and Burlaga et al. (2008) for TS3.

Fig. 1.-Mirror (solid thick line) and firehose (dash line) instability thresholds as a function of the shock angle θ Bn and strength r s for TS1 in inward motion conditions (see Table 1). These lines corresponds to C M = 1 and C F = 1 respectively (see text for definitions); the two thin lines correspond to C M = 0 and C M = 3. The heliosheath plasma is mirror (firehose) unstable for shock conditions below (above) the threshold line. Labeled regions corresponds to the five TS classes where the following processes may be observed : (1) firehose instability, (2) uniform stability, (3) possible existence of mirror stable magnetic hole structures, (4) mirror instability, (5) mirror instability with possible predominance of magnetic peak structures. The cross at r s = 3 and θ = 86 • corresponds to the TS conditions observed during V1 crossing (C M = 1.2).

Fig. 2.-Same as Figure 1 for TS1 in outward motion conditions (see Table 1).

Table 1 :

 1 Upstream parameters are from

	Upstream parameters TS1 (inward motion) TS1 (outward motion) TS3 (inward motion)
	Wind speed (km/s)	380	530	320
	Density (cm -3 )	8×10 -4	8×10 -4	0.001
	Temperature (K)	5.4×10 5	12.2×10 5	10 4
	Magnetic field (nT)	0.03	0.03	0.06
	Anisotropy (A 1 )	1	1	1
	M A1	16.3	22.7	7.6
	β 1	32.8	77.4	0.19
	Shock strength	3.0±0.2	2.5±0.2	1.58±0.71
	Shock angle ( • )	86	86	74.3±11.2

This preprint was prepared with the AAS L A T E X macros v5.2.