Anna Plesniar

Irene Malpartida

Rodrigo Moraes

Olivier Marie
email: olivier.marie@ensicaen.fr

A kinetic study of the NO to NO2 oxidation mechanism over Fe FER: a combined analysis of operando surface and gas phase data

Keywords: Mechanism, SCR, operando, Ferrierite, NOx, iron 1

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

Introduction

NOx pollution now mainly arises from road transportation: according to the European Environment Agency (EEA):

this sector produces about 40.5% of the nitrogen oxides total emission [START_REF]Nitrogen oxides (NOx) emission (APE 002[END_REF]. The abatement of this pollutant has been recently considered mainly in Diesel powered engines, whose operating conditions under an excess of air make the catalytic NOx reduction still challenging. Selective catalytic reduction (SCR) of NOX compounds by ammonia (from urea) is an efficient technology for NOx removal that however lacks of activity in the low temperature range (T < 180°C) and most often also in the high temperature range (T > 500°C). The later high temperatures are however more and more encountered when an upstream Diesel Particulate Filter (DPF) is close coupled to the SCR block. In 2009 a pioneer work thus reported the possibility to develop an SCR catalyst directly dip-coated on a DPF substrate [START_REF] Hirata | Development of an improved urea-selective catalytic reduction-diesel particulate filter system for heavy-duty commercial vehicles[END_REF]. In this context, the PM oxidation occurs on the SCR layer [START_REF] Dittler | The application of Diesel particle filters-from past to present and beyond[END_REF] and it is thus necessary to develop a thermally durable SCR catalyst since the typical stationary source catalytic formulation (V/TiO2) suffers from both the vaporisation of the vanadium active phase and the crystalline transition of the TiO2 support from anatase to rutile. A quick survey of literature data reveals that alternative NH3-SCR catalytic formulations developed for low duty vehicles are based on transition metal ion (TMI) loaded zeolites [START_REF] Sullivan | The role of Brønsted acidity in poisoning the SCR-urea reaction over FeZSM-5 catalysts[END_REF][START_REF] Park | Hydrothermal stability of CuZSM5 catalyst in reducing NO by NH3 for the urea selective catalytic reduction process[END_REF][START_REF] Grossale | NH3-NO/NO2 SCR for Diesel exhausts aftertreatment: reactivity, mechanism and kinetic modelling of commercial Fe-and Cu-promoted zeolite Catalysts[END_REF]. When considering the direct coupling of SCR onto a DPF support or resistance to ageing under high hydrothermal conditions, such zeolitic formulations [START_REF] Hirata | Development of an improved urea-selective catalytic reduction-diesel particulate filter system for heavy-duty commercial vehicles[END_REF] appear as candidate of choice with typical compositions such as Cu or Fe zeolites [START_REF] Watling | Development, validation and application of a model for an SCR catalyst coated diesel particulate filter[END_REF][START_REF] Kang | PM and NOx reduction characteristics of LNT/DPF plus SCR/DPF hybrid system[END_REF]. A combined system made of Fe/SAPO-34 and Cu/CHA is even described to exhibit very good deNOX performances in a large temperature interval (200-800°C) [START_REF] Andonova | The effect of iron loading and hydrothermal aging on one-pot synthesized Fe/SAPO-34 for ammonia SCR[END_REF].

Typically, a SCR catalyst formulation is made of acidic centres whose role consists in adsorption/activation of ammonia and red/ox centres that should provide the right NO to NO2 ratio for fast SCR to take place when the fed flow is NO rich.

(Fast SCR)

NO + NO2 + 2 NH3 = 2 N2 + 3H2O

When dealing with iron based zeolites, it is generally admitted that the NO to NO2 oxidation reaction represents the RDS of the whole SCR process. This work thus aims at determining the detailed NO to NO2 oxidation mechanism at the elemental step level on an iron loaded ferrierite (FER) preliminary aged under severe hydrothermal conditions. This investigation appears thus relevant for the evaluation of an 'underwork' DPF-SCR typical formulation and bringing insight on the mechanism at the microscopic level possibly leading to a better tuning of the active sites.

Material and methods

Catalyst preparation

An alkali form of ferrierite, NaK-FER, with a ratio of Si/Al = 8.8 (8 < Si/Al < 9.5), was provided by TOSOH Co., Japan (HSZ-700 series, FERRIERITE). The NH4-FER form was prepared by up to three ion-exchange at 353 K for 3 h under vigorous stirring, with a NH4Cl solution at a given concentration (0.10 mol.L -1 ) and using the following wtsolution/wtpowder = 75/1 ratio. After the exchange, the catalyst was washed with distilled water and dried at 373 K for 12 h.

The iron-containing catalyst was obtained by ion-exchange of the NH4 form ferrierite (NH4-FER) with a ferrous sulphate solution (FeSO4) aiming at introducing the Fe 2+ cations from the aquous solution into the zeolite pores.

The ion-exchange was performed using zeolite suspension (under continuous stirring) in diluted aqueous solution [Fe 2+ ] = 1.0 10 -3 M at a kept constant pH=2. This process is fast enough to ensure within a few hours the exchanged levels required in most application of metal zeolites. The NH4-FER zeolite (120 mg) was thus added to a continuously stirred round-bottom flask containing the FeSO4 solution (VFeSO4= 60 mL) in order to fix the mFeSO4 solution/mzeolite ratio to 500. A condensation column was connected to the flask and the solution was heated to around 80°C and stirred for 4 hours. The solution was then filtrated, under a vacuum, using a 0,45 µm filtration paper. During the filtration, distilled water was added to rinse the cake and help removing impurities dissolved in the filtrate.

Finally, the iron containing FeFER sample was submitted to an ageing procedure chosen to simulate the wet and oxidative atmosphere present at the engine exit in driving conditions with prolonged periods at rather high temperature (severe conditions). The detailed procedure of accelerated catalyst ageing under laboratorycontrolled conditions is as follows. The fresh sample was loaded in a quartz reactor placed in a tubular furnace then submitted to an ageing temperature of 800°C using a 5 K/min heating rate and a 10 hours duration step. The temperature was monitored by a thermocouple in close contact with the catalyst submitted to a total gas (10% H2O in air) volumetric flow rate of 47 cm 3 STP/min. The volume of catalyst was 1.4 cm 3 (bed height of 28 mm inside an 8 mm diameter cylinder) and therefore, the Gas hourly space velocity (GHSV) was around 2000 h -1 .

Chemical analysis of both the fresh and aged sample (now referred as FeFER800) was performed using inductively coupled plasma atom emission spectroscopy (ICP-AES) at the CNRS Centre of Chemical Analysis (Vernaison, France) and showed a constant iron loading of 0.9 wt%.

Morphology and textural analysis

The morphology of samples was studied by Scanning Electron Microscopy using a Tescan MIRA microscope.

The specific surface area was determined from physical adsorption of N2 at 77 K. The samples were first outgassed at 523 K in a dynamic vacuum for 1 h (heating rate 3 K/min). The adsorption isotherms were recorded using a Micromeritics ASAP 2020 apparatus. The low relative pressures (p/p 0 ) were explored using predefined tables (5.10 -7 < P/P° < 1) with an automatic control of the N2 added amounts. The total pore volume was determined at p/p 0 = 0.99. The monolayer volumes (approximated as the microporous volumes) were estimated using both the Brunauer-Emmett-Teller (BET) and the Langmuir models for P/P° < 0.03. Finally, the t-plot equation was applied in order to provide a further value for the monolayer volumes.

IR operando tests

For the operando experiments, a 'sandwich like' IR cell-reactor fitted with a recently designed square sample holder was used [START_REF] Thomas | Modelling a reactor cell for operando IR studies: From qualitative to fully quantitative kinetic investigations[END_REF]. Such a modified sample holder indeed leads to a virtually perfect plug-flow reactor, which simplifies data computing, provides a better fit of the experimental data and more accurate estimates of the kinetic parameters. The experimental set-up is based on a central six ways valve allowing to submit the catalyst (shaped as a 13 mg wafer pelletized under 0.50 tons/cm 2 leading to a 40 µm thickness) to an activation procedure while simultaneously preparing and stabilizing the reaction flow. The above described catalyst shape and IR reactor cell configuration allow according to Rasmussen et al [START_REF] Rasmussen | Does pelletizing catalysts influence the efficiency number of activity measurements? Spectrochemical engineering considerations for an accurate operando study[END_REF] to lead a kinetic study as relevant as one performed in quartz fixed bed reactor.

Before the experiments the catalysts were pretreated at 400 °C in Ar at a constant total flow rate of 20 mL min -1 for 1 h. The Plug Flow Reactor (PFR) cell was operated in the differential mode by restricting the NO conversion to f<10%. The inlet NO molar fraction was varied in the [100-2000 ppm] range while the O2 molar content was kept constant at 14% (diluted in Ar). All the experiments were conduced under atmospheric pressure and three reaction temperatures were tested (100, 130 and 160°C) in the [180 000 -240 000 h-1 ] space velocity range. The NO and NOx (NO + NO2) concentrations in the outlet gas were detected with a chemiluminescence detector (Thermo Scientific Megatec Model 42i-HL).

The IR spectra relative to the catalyst under duty were collected with a Nicolet Magna 750 FT-IR spectrometer, equipped with MCT detectors. In order to ameliorate the signal/noise ratio, the number of scans accumulation was set to 64 at a spectral resolution of 4 cm -1 .

Results and Discussion

3.1

Impact of the ageing on the morphology and the texture

Evolution of morphology from FeFER to FeFER800

As shown on Fig. 1 (left part), the 'fresh' FeFER powder is made of 'sheet' or 'plate' like individual particles that stuck together form 'egg' like spherical agglomerates with a rather smooth external surface. A zoom on this external agglomerate surface showed that it was made of an almost perfect 'puzzle like' pavement (not shown). It was thus interesting to test whether this external surface remained as smooth as in the 'fresh' sample after ageing was conduced. The Fig. 1 right part perfectly illustrates that for the FeFER800 sample, the agglomerates external surface roughness has considerably increased. For sure, it is quite difficult, (even from a few tens of pictures) to reasonably quantify the degree of roughness creation, but the analogy with a pine cone clearly reveals a general trend indicating that pine cone opening progresses upon increasing temperature up to 800°C. As a conclusion, it appears that the hydrothermal treatment favor the dislocation of agglomerates. Two hypothesis may explain this phenomenon: i) the presence of water in high temperature conditions would favor the hydrolysis of the rather soft bonds between the individual particles or/and ii) the increasing pressure inside the agglomerates upon heating would provoke the shell 'explosion'.

Evolution of textural properties from FeFER to FeFER800

The evaluation of the effects of the ageing procedure on the textural properties of the catalysts was carried out using the standard N2 physisorption at liquid nitrogen temperature.

For plots relative to both FeFER and FeFER800, the isotherm was typical for the type I one (also called Langmuir isotherm) for which the adsorbed volume readily reaches a plateau (P/P o < 0.2). The isotherm data were processed according to several theories (Langmuir, BET and t-plot) in order to estimate the microporous volumes.

The total porous volume was directly obtained from the isotherm at P/P° = 0.99 (which corresponds to the filling of pores with size below 100 nm) and then the sum of mesoporous and macroporous volumes was determined by difference. Summaries of the estimated microporous and mesoporous volumes according to the various applied isotherm processing are presented in Table 1. The previous data obtained form SEM indeed indicate that hydrothermal treatment favours the dislocation of agglomerates. This result explains properly the evolution of the meso/macroporous volume upon ageing but is not 'a priori' sufficient to justify the increase of the microporous system. The individual ferrierite crystals morphology has thus been considered. According to Tschernich [START_REF] Tschernich | Zeolites of the world[END_REF], orthorhombic ferrierites are made of blades (plates or sheets) elongated along the c-axis and with commonly the {100} as the dominant plane. Taking then into account that the main 10 members ring channels run along the c-direction, it is possible to propose a model in which, for a fresh sample, a compact given agglomerate is made of a rather perfect pavement of single crystals whose staking along the c-direction is randomly imperfect, thus leading to 10 m.r. pore entrance blocking. Upon hydrothermal ageing, the agglomerate dislocation ('pine cone' opening) proceeds (see Figure 1 right part) and consequently more isolated individual crystals present a higher available microporous volume.

Preliminary tests before kinetic experiment

The determination of a reaction mechanism should not only provide information relative to the nature of active sites, the reaction intermediates but also should allow the development of a kinetic model enabling to properly describe the experimental data. However, the development of a kinetic model from a mechanism provides equations that lead to relevant and useful values only if the experiments are conduced in the chemical regime.

A set of preliminary experiments was thus achieved with the FeFER fresh sample in order to ensure that external mass transport limitations do not occur after shaping the powder in the wafer form. For this purpose, the total volumetric flow rate was varied but the contact time was kept constant by adjusting the amount of catalyst. The results are described below on Figure 2 and obviously the reaction rate remained constant under these conditions so that external mass transport gradients may be assumed negligible [START_REF] Vannice | Kinetics of catalytic reactions[END_REF]. In the regime of pore (intra-crystalline) diffusion control, the observed rate is proportional, in essence, to the ratio of the external surface to the volume of the catalyst particles. In order to evaluate the extent of internal diffusion control it is thus necessary to perform catalytic tests using zeolites with similar chemical composition but different particle size. This not an easy task and the synthesis only would require a complete dedicated study. Recent literature data were thus considered and it was found that over Cu-SSZ-13 the NH3 oxidation reaction was in the chemical regime for reaction temperatures below 250°C [START_REF] Gao | Structureactivity relationships in NH3-SCR over Cu-SSZ-13 as probed by reaction kinetics and EPR studies[END_REF]. Both particles size (µm range) and GHSV (200 000 -800 000 h -1 ) are there comparable to those reported in the present work and it was here reasonably assumed that working in the [100-160°C] range for the NO to NO2 oxidation reaction should prevent from internal diffusion limitation.

Finally, the next part of the study will focus exclusively on the aged FeFER800 for the main reason exposed above relative to the real life of a DPF-SCR formulation. Taking into account the morphology and textural results, it then appears obvious that the 'pine cone opening' effect will further improve both the inter-particle diffusion (higher mesoporosity) and the intra-particle diffusion (higher available microporous volume) towards the iron active sites. Preliminary verifications are thus validated and further kinetic modelling arising from distinct possible mechanisms makes sense.

Catalytic data

This part will be dedicated to the description of the 'bare' catalytic data obtained from both the gas phase and the catalyst surface (operando) analysis over the FeFER800 catalyst.

For these experiments the mass of catalyst was w = 12.80 mg, the NO inlet molar fraction was modified while the total flow was set to 50 NmL.min -1 (unless indicated differently). The following Table 2 reports both the inlet NO partial pressure (PNO), the NO to NO2 conversion (noted f), the specific initial reaction rate (r°) and the IR band intensity (peak height) for mononitrosyl (normalized to 1 mg of powder) where r° = FNO,in * f / w.

FNO,in stands for the NO inlet molar flow. The Figure 3 indeed illustrates as a typical example, the evolution of the infrared spectra relative to adsorbed species detected when the NO to NO2 reaction proceeds at 100°C over FeFER800. The change of the inlet NO concentration clearly leads to a variation of the band intensity. The most intense peak appears at 1878 cm -1 and is assigned to Fe 2+ mononitrosyl species arising from the interaction of NO with iron cations located at site G of the FER structure [START_REF] Ivanova | Evidencing three distinct Fe II sites in Fe-FER zeolites by using CO and NO as complementary IR probes[END_REF][START_REF] Blasin-Aube | Iron nitrosyl species in Fe-FER: a complementary Mossbauer and FTIR spectroscopy study[END_REF]. The region where produced NO2 and its subsequent adsorption products are expected presents several components: two sharp ones at 1625 and 1612 cm -1 and a shoulder at 1575 cm -1 . A clear assignment to identified species tends to be complicated due to quite different data in the literature. For example, even if the presence of water traces in the flow can not totally be ruled out, the band located at 1625 cm -1 may also arise either from a bridging Al-nitrate species [START_REF] Szanyi | Effect of H2O on the adsorption of NO2 on gamma-Al2O3: an in situ FTIR/MS study[END_REF][START_REF] Underwood | Transmission FT-IR and Knudsen cell study of the heterogeneous reactivity of gaseous nitrogen dioxide on mineral oxide particles[END_REF] or from a species attached to extra-framework Fe-Al-O [START_REF] Hensen | Extraframework Fe-Al-O species occluded in MFI zeolite as the active species in the oxidation of benzene to phenol with nitrous oxide[END_REF]. The 1612 cm -1 component can possibly be assigned to NO2 adsorbed onto cationic species [START_REF] Hadjiivanov | Identification of Neutral and Charged NxOy Surface Species by IR Spectroscopy[END_REF] but the analysis of the 1612 and 1575 cm -1 bands illustrates a similar evolution thus suggesting they may characterize one single species, probably an iron/aluminum based nitrate. The three later bands thus typically originate from NO2 interaction most probably with EFAL species and it is here assumed that they do not compete for adsorption onto iron active site.

As a consequence, the Table 1 only represents the evolution of the band intensity for iron mononitrosyls [*Fe_NO] here considered as the Most Abundant Reaction Intermediate species.

Hypothetical reaction mechanisms

In the next part of this work, five hypothetical mechanisms will be processed according to an exhaustive kinetic study. The Fig. 4 represents the various mechanisms that were tested in this study. This for sure does not represent an exhaustive list and the emphasis was put on both original hypothesis and already proposed mechanisms. The choice regarding the distinct possible hypotheses was guided by the nature of the active sites.

It is indeed worth knowing, for a better tuning of the catalyst formulation, whether isolated, oligomeric or dual iron sites are involved in the catalytic loop. Different possibilities were thus investigated. The three first original hypotheses thus all require active sites close proximity. At least, dual iron sites are necessary for hypothetical mechanism 1 and 3 to take place while oligomeric species are necessary for hypothesis 2. On the contrary, hypotheses 4 and 5 involve isolated iron sites that are favoured inside the zeolite microporosity. The first proposed hypothesis is an original and very basic one in which O2 does not adsorb on the catalyst but directly reacts with two neighbouring adsorbed NO according to a Eley-Rideal mechanism [21]. Hypothesis 2 involving a reaction between two adsorbed species is typical for a Langmuir-Hinshelwood mechanism. Hypothesis 2 is also original and considers not only NO adsorption but also O2 dissociative adsorption on the catalyst.

Hypothesis 3, 4 and 5 involve the interaction between an adsorbed species and a gas phase molecule and could be labelled as Eley-Rideal ones. Even if more rarely met than Langmuir-Hinshelwood mechanism, the presence of isolated single sites inside zeolites onto which only one reactant may be activated in the adsorbed state justifies the test of the Eley-Rideal mechanism. The Hypothesis 3 is original and requires the dissociative NO adsorption while mechanisms 4 and 5 come from previous works [START_REF] Weiss | Mechanism and site requirements for NO oxidation on Pd catalysts[END_REF][START_REF] Brüggemann | Theoretical investigation of the mechanism of the oxidation of nitrogen oxide on iron-form zeolites in the presence of water[END_REF]. The fifth hypothesis, considering the co-adsorption of NO and O2 onto the same iron site has recently been revised from a theoretical point of view [START_REF] Brüggemann | Theoretical investigation of the mechanism of the oxidation of nitrogen oxide on iron-form zeolites in the presence of water[END_REF] while previous experimental studies had previously suggested such a mechanism [START_REF] Brosius | NO oxidation kinetics on iron zeolites: influence of framework type and iron speciation[END_REF][START_REF] Capek | Kinetic experiments and modeling of NO oxidation and SCR of NOx with decane over Cuand Fe-MFI catalysts[END_REF].

It seemed important, in the frame of this study, to provide all the details regarding the theoretical development of the various kinetic expressions. However, considering the whole elemental steps as possible rate determining ones for each mechanism, more than one hundred equations were obtained. As it would be fastidious to consider carefully the whole content in the core of this article, it was decided to move most of the equation development in a Supplementary Information file. In order to explain the applied methodology, the next paragraph will nevertheless detail how were obtained the rate equations for mechanism 1 in the specific case of the chemical reaction being considered as the Rate Determining Step. A summary of the possible plots and associated (hypothesis + RDS) couples will then be reported.

Detailed analysis for mechanism 1: RDS considered as surface reaction from *Fe_NO

In the context of this RDS, the other steps are considered at pseudo-equilibrium and the corresponding set of consecutive elemental steps is described below:

where *Fe are free superficial active sites, Kads NO is the adsorption equilibrium constants for NO, Kads NO2 the adsorption equilibrium constants for NO2 and k2 the kinetic constant relative to step 2.1 considered here as the non reversible rate determining step (RDS). Generally speaking in the rest of this work, the step (i.j) notation will stand for step i of hypothetical mechanism j.

In the frame of this RDS, the reaction rate can be expressed as: should follow a linear evolution with available via an Arrhenius plot:

The Fig. 5 upper part reports the typical plot 1 obtained at three distinct temperatures. Complementary, the 'classical' kinetic treatment of the 'single' gas phase data should allow to confirm/infirm the proposed RDS for the chosen mechanism. Adsorption steps 1 and 3 are quasi-equilibrated, so:

eq. 2 = !"_ * # !" * # $ eq. 3 = !"_ * # !" * # $
Adsorbed species similar to those previously described in the frame of this mechanism are still present under reaction conditions, and thus we still have: Taking then into account the differential conditions (conversion f < 10% in most cases and even if some values reported in Table 2 are slightly higher, they are still compatible with the assumption of differential regime), the reaction rate is finally given by the following expression (the PNO2 containing term in the denominator of eq. 5 has Working in the differential mode of the PFR also enables to simplify PNO = PNO inlet and as a constant high excess of oxygen (with respect to stoichiometry) was used, the consistency of the hypothesis could be tested since: while the (slope plot 2 / y-intercept plot 2) ratio directly provides Kads NO at a given temperature. Thus, synthesizing the data obtained at several temperatures allowed to estimate both the reaction activation energy ( = 43 kJ.mol -1 ) and the NO adsorption heat (∆Hads NO = -30 kJ.mol -1 ) through Arrhenius and Van't Hoff plots respectively. These values provide useful estimations for further modelling of the whole temperature data.

a RDS E 14

A summary of the various possible plots after an exhaustive study of the five hypotheses

As indicated above, the full description of the detailed analysis for the four remaining hypothetical mechanisms would be fastidious here and the whole results are provided in a Supplementary Information file.

Indeed more than one hundred distinct equations were necessary to properly obtain the reaction rate equations relative to each of the elemental step as a possible RDS one for the whole hypothetical mechanisms. However, when processing the various reaction equations through linearization in order to get a first evaluation of the hypothesis validity, only six distinct plots were obtained for the operando (catalyst surface) data involving the intensity of adsorbed mononitrosyl species. Similarly, the reaction rate equations arising from the gas phase data lead to only five distinct plots after linearization. The table 3 provides a summary of the distinct possible plots. It is filled with the rate determining steps obtained for each given hypothesis, satisfying both the plots obtained from the operando data (column) and the gas phase data (raw).

Gas phase data

Table 3. A summary of operando (catalyst surface) and gas phase crossed data obtained for NO to NO2 reaction over FeFER800. In order to provide a 'user manual' for Table 3, a simple example is given below. Assuming that step 2 of mechanism 1 is the rate determining step (RDS 2.1), the experimental data should satisfy both a linear plot 1: Inversely, considering the best agreement between the experimental data and the linear plots (from the determination coefficient at a first rough estimation), for both the operando results (see Fig. 6) and the gas phase results (see Fig. 7), it is possible to limit the amount of relevant RDS.

Operando data

r T = g V Fe_NO * [ \ r T = g 8 Fe_NO * # 2 A r T = g] Fe_NO * #^ r T = g V Fe_NO * P `a bcdef \ r T = g V Fe_NO * P `a bcdef \ = V _ * [ \ r T = g P `a bcdef RDS 1.1 Fe+NO-
The detailed analysis of Fig. 6, 7 and Table 3 should also be rejected.

According to the above results, the following plots SI 9, SI 11, SI 14 and SI 16 will then be disregarded and the non-relevant corresponding equations will not be considered anymore.

Towards the best hypothesis and its associated kinetic parameters

The preliminary fast data processing using linear regressions allowed a reduction of the number of plots to be further considered through very simple criteria: negative values of slope incompatible with the model or very low values of the determination coefficient R 2 . However, when aiming at discriminating the best model, considering the R 2 value as close as possible from unity is not a reliable enough criterion. Indeed, it is worth for each possible plot to calculate a theoretical reaction rate rm,theo starting form values estimated through linear regression and to optimize the constant relative to the model via the minimization of the standard deviation error (SD) defined as:

rs = g ∑]u v,RxyQ zu v,y{O ^7 |zN
where n represents the number of experimental points and p the number of adjustable parameters. The table 4 presents the results obtained when considering independently the operando and the gas phase data. When considering first the operando data, it is worth noting that for the whole plots, the rate is a linear function of a variable including the [*Fe_NO] concentration with a y-intercept fixed to zero. As a consequence, the SD values are directly provided by the Excel © LINEST function since the slope optimisation through non-linear routine is not possible. A quick comparison of the obtained SD values clearly indicates that plot SI 25 leads to the highest SD being about twice the ones calculated for the other plots. It is thus decided to reject the hypothesis leading to plot SI 25 and the associated equations. A look at table 3 reveals that when the operando plot SI 25 is rejected, the gas plot SI 2 should also be rejected.

Indeed, when the gas data shown at table 4 are considered, the highest SD value obtained for plot SI 2 (about 4

times the one obtained for other plots) confirms that it should not be considered anymore. Concerning plot 2 and plot SI 4, non-linear optimization of slope lin and y-intercept lin through minimization of the SD values were performed using the Excel © SOLVER tool. New values for slope opt and y-intercept opt were then obtained and the comparison of the minimized SD values indicates that plot SI 4 appears to be slightly better than plot 2 contrarily to what would have been concluded from simple comparison of R 2 values (see Fig. 7).

At this step of the study, only remain as possible plots, 1, SI 1 and SI 3 for the operando data and 2 and SI 4 for the gas phase data. However, a focus on the grey zone of table 3 reveals that nine among nineteen distinct RDS (i.j) still remain as good candidates. Aiming at identifying the best one, the next step will thus consist for each remaining possible RDS (i.j) in processing simultaneously both the whole data (operando + gas) and the whole temperatures. Indeed, when a given reaction mechanism and its identified RDS are relevant, the theoretical fit of the experimental data should be valid whatever the temperature according to Arrhenius/Van't Hoff law. The example for RDS (2.1) will be detailed below while a summary table will then be provided for brevity seek.

RDS (2.1) whole data processing.

The equations relative to step 2 considered as the RDS for hypothetical mechanism 1 were exhaustively described in the core of the paper. Concerning the rate as a function of [*Fe_NO], the eq. 1 was obtained while eq. 6 describes the rate as a function of gas phase data only (see section 3. Aiming at considering the whole temperatures simultaneously, eq. 1 and eq. 6 convert into eq. 8 and eq. 9 respectively.

eq. 8

= 2 ~2 • -• 'sr ƒ '" … B 2 * _ 2 eq. 9 = 2 ~2 j -• 'sr ƒ '" q B 2 + 2 † 2 ‡ -2 Δ‰ ƒŠ‹ '" OE B 2 • Ž • 1+ † ‡ -Δ‰ ƒŠ‹ '" OE B • ' ' 2
where A2 and B stand for pre-exponential factors in the Arrhenius expression of the k2 kinetic constant and the Van't Hoff expression of the Kads NO thermodynamic constant respectively.

In order to calculate the reaction rates obtained in the whole temperature range from both operando and gas phase data, estimated values for five independent parameters (A2, B, LFe, ERDS and ∆Hads NO) should first be estimated.

Preliminary processing of the gas phase data provided estimated values for = 43 kJ.mol -1 and for NO adsorption heat ∆Hads NO = -30 kJ.mol -1 (see section 3.3.3).

Estimate for 2 A2 PO2 LFe 2 was obtained from the slope of the following plot:

plot 3 8 ' F""" "F"G • A = -V" • -˜™ š› ™• … \
Estimate for B was obtained from the slope of the following plot:

plot 4 oe•žŸ Ÿ•ž ¡ ¢z£¤ ¥ Ÿ Ÿ•ž ¡ = ¦ ‡ V - §¨© ªoe «¡ \ OE
Estimate for LFe 2 was obtained from the slope of the following plot:

plot 5 8 ' F""" "F"G • A = -F""" "F"G ' •
Table 5 reports the whole estimated values together with their optimized values obtained after minimization of SD for the reaction rate calculated using both eq. 8 and eq. 9. a RDS E A similar methodology was applied for the eight remaining possible RDS (i.j). The number of parameters required to model the whole experimental data was always fixed to the minimum value (see first column of Table 6) and their initial estimated values were always in a reasonable range as indicated by the initial estimated standard deviation lying between 1.27 10 -4 and 7.70 10 -4 . Analysing the SD optimized values reported in Table 6 in more details, it appears that RDS (2.1) at the intersection between plot 1 and plot 2 (Table 3) and RDS (5.5) at the intersection between plot SI 1 and plot SI 4 (Table 3) should be rejected in agreement with their corresponding high ΣSD values reported in Table 4. As a consequence, only RDS at the intercept between plot SI 3 and plot SI 4 (grey zone in Table 6) remain the most possible. The optimized SD values are however very closed the ones from the others (6.36 10 -5 < SD < 7.02 10 -5 ) and a supplementary criterion will be welcome in order to identify the best hypothesis. Indeed, among the seven remaining hypothesis, four of them [(3.1), (4.2), (5.3) and (3.4)] involve the NO2 desorption from iron as the RDS.

Consequently, at a given temperature, the initial reaction rate should increase with the concentration of adsorbed NO2 here noted as [*Fe_NO2]. When processing the operando spectra reported at Fig. 3 the focus was put on the quantitative analysis of the mononitrosyl species band intensity that is proportional to their concentration [*Fe_NO]. However, the spectra were also qualitatively described and even if band assignment was proposed as nitrate species for the 1620 cm -1 and adsorbed NO2 for the 1612 one, it is worth noting that both bands may also characterize adsorbed NO2 onto cationic site according to Hadjjivanov [START_REF] Hadjiivanov | Identification of Neutral and Charged NxOy Surface Species by IR Spectroscopy[END_REF] and ref therein. Starting from this new assignment and considering hypothetical RDS (3.1), (4.2), (5.3) and (3.4), one should then observe an increase of the 1612 and 1620 cm -1 band intensity with the reaction rate. The semi quantitative analysis of Fig. 3 clearly shows that this is not the case. Indeed, Table 2 provides evidence that the reaction rate increases with [*Fe_NO] while Fig. 3 shows an opposite evolution between the 1878 cm -1 typical for [*Fe_NO] and the 1620-1612 cm -1 bands typical for [*Fe_NO2].

As a conclusion, if any adsorbed *Fe_NO2 are present on the FeFER800 catalyst under duty, their evolution does not match with their desorption being the RDS. Hypothetical RDS (3.1), (4.2), (5.3) and (3.4) should then be rejected.

Only three RDS then remain as good candidates: RDS (2.4), (2.5) and (3.5). Concerning RDS (2.4), as it involves Fe_O species that are not detected here by IR spectroscopy, we can not confirm or infirm this hypothesis.

However, RDS (3.5) and RDS (2.4) require exactly the same number of parameters [START_REF] Watling | Development, validation and application of a model for an SCR catalyst coated diesel particulate filter[END_REF] for modelling the whole data. The SD value is thus calculated exactly the same way (similar denominator) and since the former RDS (3.5) leads to a slightly lower SD value than the later, the RDS (2.4) will further be rejected in the present work.

Considering now RDS (2.5) and RDS (3.5), it is worth noting that the last one leads to the lowest optimized SD value. Moreover, RDS (2.5) and RDS (3.5) both relate to the same reaction mechanism whose RDS was previously described as the Fe_OONO dissociation into Fe_O and NO2 [START_REF] Brüggemann | Theoretical investigation of the mechanism of the oxidation of nitrogen oxide on iron-form zeolites in the presence of water[END_REF]. This step exactly consists in our RDS (3.5) and our experimental data together with their original kinetic processing thus perfectly match with previous theoretical modelling. It is however important to specify that few modifications were made regarding the detailed mechanism proposed by Brüggemann et al [START_REF] Brüggemann | Theoretical investigation of the mechanism of the oxidation of nitrogen oxide on iron-form zeolites in the presence of water[END_REF] in order to fit with our operando data. More precisely, the Fe_OONO intermediate species was here noted as Fe_NOO2 as a result from the interaction between the observed Fe_NO and O2 from the gas phase. Finally, a good candidate for the IR band typical for this Fe_NOO2 active intermediate species is the 1575 cm -1 one even if its low intensity and location at the tail of the broad 1620-1612 cm -1 doublet prevent from reliable quantitative analysis.

The best RDS was thus identified as the third step of mechanism 5. The values for the seven parameters required to calculate the corresponding reaction rate either form eq. SI 114 or eq. SI 117 are provided in Table 7.

eq. SI 114

r T = k -K ¯`a P a 7 Fe_NO * eq. SI 117

r T = °± ² ³´ = µ;< : < 7 = >?@ ;< : ;< 9(]= µ;< : < 7 (9^= >?@ ;< : ;< The top part of Table 7 summarizes the initial data set and the estimated values that were used as input before running the several iterations required to get the minimal SD value reported in Table 6. It seems important here to remind that the molar extinction coefficient for the mononitrosyl species Fe_NO was not determined and that the

[Fe_NO] values used for the data modelling are the bare heights of the IR peak normalized per mg of powder (in mg -1 ) that are indeed proportional to molar specific concentrations. For dimensional concordance, the total specific iron concentration LFe opt is thus also obtained in mg -1 and as a consequence the A3 opt value is obtained in mmol.h -1 . The only right parameter is thus the A3 opt LFe opt product whose value equals 3.64 10 +1 mol.h -1 .g -1 . Given the nominal iron weight loading (0.90 wt%), it is then possible to estimate LFe real = 1.61 10 -4 mol.g -1 and get a value for A3 real = 2.26 10 +5 h -1 .

Finally, the Fig. 8 provides the whole experimental data obtained in this work together with their best fit obtained using the optimized values reported in Table 7. Both the reaction rate as a function of surface mononitrosyl concentration (upper part) and the reaction rate as a function of PNO (lower part) theoretical curves (in red) present a rather goof fit of the experimental points. The curve fitting quality obviously increases with the reaction temperature and one suggests that traces of water impurities may affect the reaction mechanism [START_REF] Brüggemann | Theoretical investigation of the mechanism of the oxidation of nitrogen oxide on iron-form zeolites in the presence of water[END_REF] specially in the low temperature range. 7.

Conclusions

involving the complementary kinetic processing of both operando and gas phase data is reported in the context of automotive depollution. This approach involving operando data in the kinetic processing is however highly promising. It was indeed also successfully applied in the context of alkane monomolecular cracking [START_REF] Kadam | Impact of zeolite structure on entropic-enthalpic contributions to alkane monomolecular cracking: an IR operando study[END_REF][START_REF] Li | Monomolecular cracking rates of light alkanes over zeolites determined by IR operando spectroscopy[END_REF]. 7.

5.

Figure 1 :

 1 Figure 1: SEM pictures for the fresh FeFER (left) and aged FeFER800 right (upper part). Analogy with a pine cone opening to illustrate the surface roughness creation (bottom part).

Figure 2 .

 2 Figure 2. Verification of the absence of external diffusional limitation for the 'fresh' FeFER catalyst (W-mass of the catalyst and G-total volume NTP flow increased from 40 mL.min -1 to 80 mL.min -1 )

  of operando surface and gas phase data to evaluate the NO to NO2 oxidation mechanism

Figure 3 .

 3 Figure 3. Iron nitrosyls intensity as a function of NO gas concentration at 100°C over FeFER800.

Figure 4 .

 4 Figure 4. Five distinct hypothetical mechanisms for NO to NO2 oxidation and their sequence of elemental steps

Figure 5 .

 5 Figure 5. Kinetic processing of data obtained over FeFER800 in the frame of RDS (2.1) at distinct temperatures (Left) 100°C, middle (130°C) and right (160°C). Upper part: Plot 1 relative to operando adsorbed species. Lower part: Plot 2 relative to gas phase data.

6 = 2

 62 been neglected which corresponds to [*Fe_NO2] << [*Fe_NO] ant traduces that iron nitrosyl are the most abundant reaction intermediate MARI): eq.

  DEF"Gshould be a linear one with non zero value for the y-intercept.The Fig.5lower part reports the typical plot 2 obtained at three distinct temperatures. Contrarily to what is observed for plot SI 2, the experimental dispersion is here low and values for the determination coefficient R 2 are always close to unity. The (2.1 hypothesis + RDS) couple thus provides a good candidate to properly describe the catalytic behaviour. From the slope, values proportional to k2 were obtained at a given temperature according to

Figure 6 .

 6 Figure 6. A summary of the possible plots arising from the kinetic processing of operando data over FeFER800; Temperature: Upper row 100°C, middle row 130°C, lower row 160°C.

  DEF"G . The RDS 2.1 is thus indicated in the cell at the intercept between the corresponding column and raw.

Figure 8 .

 8 Figure 8. Best experimental data fit (in red) of the NO to NO2 oxidation rate (RDS 3.5) obtained over FeFER800 as a function of [*Fe_NO] (Upper part) and PNO (Lower part). The whole temperature data (Left) 100°C, middle (130°C) and right (160°C) were fitted with the optimized individual parameters reported in Table7.

Figure 1 .

 1 Figure 1. SEM pictures for the fresh FeFER (left) and aged FeFER800 right (upper part). Analogy with a pine cone opening to illustrate the surface roughness creation (bottom part).

Figure 2 .

 2 Figure 2. Verification of the absence of diffusional limitation for the 'fresh' FeFER catalyst (W-mass of the catalyst and G-total flow).

Figure 3 .

 3 Figure 3. Iron nitrosyls intensity as a function of NO gas concentration at 100°C over FeFER800.

Figure 4 .

 4 Figure 4. Five distinct hypothetical mechanisms for NO to NO2 oxidation and their sequence of elemental steps.

Figure 5 .

 5 Figure 5. Kinetic processing of data obtained over FeFER800 in the frame of RDS (2.1) at distinct temperatures (Left) 100°C, middle (130°C) and right (160°C). Upper part: Plot 1 relative to operando adsorbed species. Lower part: Plot 2 relative to gas phase data.

Figure 6 .

 6 Figure 6. A summary of the possible plots arising from the kinetic processing of operando data over FeFER800; Temperature: Upper row 100°C, middle row 130°C, lower row 160°C.

Figure 7 .

 7 Figure 7. A summary of the possible plots arising from the kinetic processing of gas data over FeFER800; Temperature: Upper row 100°C, middle row 130°C, lower row 160°C.

Figure 8 .

 8 Figure 8. Best experimental data fit (in red) of the NO to NO2 oxidation rate (RDS 3.5) obtained over FeFER800 as a function of [*Fe_NO] (Upper part) and PNO (Lower part). The whole temperature data (Left) 100°C, middle (130°C) and right (160°C) were fitted with the optimized individual parameters reported in Table7.

Table 1 .

 1 Textural characterization results for the 'fresh' FeFER and aged FeFER800 samples.

Sample Hydrothermal and oxidative ageing 10 hours Microporous volume (mL.g -1 ) Mesoporous + macroporous volume (mL.g -1 ) Langmuir BET t-plot

	FeFER	0.124	0.120	0.124	0.156
	FeFER800	0.139	0.134	0.141	0.185
	It is obvious first that for any considered sample, all the applied theories are in good agreement regarding the
	values obtained for the microporous volume. Furthermore, data unambiguously indicate that both the microporous
	and meso/macroporous volume increased upon severe hydrothermal treatment. This trend is unexpected if we
	consider data form the literature indicating that hydrothermal treatments provoke framework dealumination
	leading to the formation of extra-framework aluminium species (EFAL). Those EFAL remaining inside the
	microporous system should contrarily to what is observed lower the available microporous volume.

Table 2 .

 2 A compilation of catalytic data obtained for NO to NO2 reaction over FeFER800. Total flow = 50 mL.min -1 except for xNO labelled with ‡ where total flow = 39 mL.min -1 .

	Temperature /°C	xNO / ppm PNO / atm	f / %	r° / mol.h -1 .g -1	[*Fe_NO] / a.u
		178	1.78 10 -04	10.2	1.75 10 -04	2.55 10 -01
		257	2.57 10 -04	8.3	2.04 10 -04	2.87 10 -01
		434	4.34 10 -04	6.1	2.54 10 -04	3.27 10 -01
	100
		601	6.01 10 -04	4.8	2.77 10 -04	3.48 10 -01
		888	8.88 10 -04	4.2	3.58 10 -04	3.70 10 -01
		1403	1.40 10 -03	3.6	4.84 10 -04	3.67 10 -01
		252	2.52 10 -04	17.2	4.16 10 -04	1.78 10 -01
		426	4.26 10 -04	13.3	5.43 10 -04	2.19 10 -01
		595	5.95 10 -04	9.6	5.48 10 -04	2.57 10 -01
	130
		880	8.80 10 -04	8.5	7.18 10 -04	2.77 10 -01
		1370	1.37 10 -03	6.5	8.54 10 -04	3.20 10 -01
		1537	1.54 10 -03	6.3	9.29 10 -04	3.24 10 -01
		395	3.95 10 -04	23.0	8.72 10 -04	1.36 10 -01
	160	555	5.55 10 -04	19.6	1.04 10 -03	1.66 10 -01
		857	8.57 10 -04	16.2	1.33 10 -03	2.09 10 -01

  thus enables to clearly reject the RDS 2.2 and 1.4 as right ones DEF"G presents a negative value for its slope (whatever the reaction temperature) which is inconsistent with the theory (see pages 10 and 31 of SI file). As a consequence, plot SI 11 together with plot SI 9 whose RDS are common with those for plot SI 11 (see table3) should be rejected.

	since the plot SI 11: C = K $ RDS 2.3 and 3.2 should also be rejected even if the C ' H I	$ DEF"G H I	= K $ DEF"G plot is reasonable at 160°C.
	Indeed, the complementary plot SI 14: i = g j	k Fe_NO * P NO inlet	l	2

q arising from operando results presents very low determination coefficient values (0.572 < R 2 < 0.883) when the intercept at the origin is forced to zero. As a consequence, plot SI 14 together with plot SI 16 whose RDS are common with those for plot SI 14 (see table

[START_REF] Dittler | The application of Diesel particle filters-from past to present and beyond[END_REF]

Table 4 .

 4 A summary of SD values for remaining possible plots both for operando (catalyst surface) and gas phase data obtained for NO to NO2 reaction over FeFER800.

			Temperature
			/°C	slope lin	slope opt	y-intercept lin y-intercept opt	SD	} rs
			100	4.48 10 -5	-	-	-	4.70 10 -5
									3.67
		Plot SI 1	130	1.95 10 -4	-	-	-	1.55 10 -4
									10 -4
			160	1.03 10 -3	-	-	-	1.65 10 -4
			100	2.74 10 -3	-	-	-	6.11 10 -5
									3.35
		Plot 1	130	9.00 10 -3	-	-	-	8.64 10 -5
	operando		160	2.93 10 -2	-	-	-	1.96 10 -4	10 -4
	data		100	9.16 10 -4	-	-	-	8.14 10 -5
									2.35
		Plot SI 3	130	2.58 10 -3	-	-	-	7.08 10 -5
									10 -4
			160	6.85 10 -3	-	-	-	8.31 10 -5
			100	1.84 10 -6	-	-	-	9.35 10 -5
									7.05
		Plot SI 25	130	1.30 10 -5	-	-	-	2.75 10 -4
									10 -4
			160	1.49 10 -4	-	-	-	3.37 10 -4
			100	3.99 10 -1	-	-	-	8.33 10 -5
									5.86
		Plot SI 2	130	6.93 10 -1	-	-	-	1.88 10 -4
									10 -4
			160	1.21	-	-	-	3.15 10 -4
	Gas		100	40.9	41.3	8.59 10 -3	8.61 10 -3	4.43 10 -5	1.49
	data	Plot 2	130	29.5	29.6	6.20 10 -3	6.19 10 -3	6.17 10 -5	10 -4
			160	19.8	19.8	6.04 10 -3	6.05 10 -3	4.31 10 -5
			100	1.52 10 +3	1.47 10 +3	0.972	1.03	3.43 10 -5
									1.09
		Plot SI 4	130	8.05 10 +2	8.10 10 +2	0.482	0.480	4.97 10 -5
									10 -4
			160	3.48 10 +2	3.47 10 +2	0.331	0.333	2.34 10 -5

Table 5 .

 5 Optimization of the kinetic parameters when considering RDS(2.1)

		Estimated values	Optimized values
	2 A2 PO2 LFe 2	401	5.91 10 +3
	E a RDS / kJ.mol -1	43.0	52.4
	B	0.383	1.32 10 -3
	∆Hads NO / kJ.mol -1	-30.0	-52.3
	L Fe 2	9.18 10 -2	9.80 10 -2
	SD	2.68 10 -4	1.12 10 -4
	3.3.5.2 Summary for whole data processing.

Table 6 .

 6 Comparison of the SD values obtained after processing the whole data (various T and operando + gas)

	when considering the remaining possible RDS (i.j)
	Hypothesis -number of
		SD estimated values	SD optimized values
	necessary parameters
	RDS (2.1) -5	2.68 10 -4	1.12 10 -4
	RDS (3.1) -7	7.60 10 -4	6.59 10 -5
	RDS (4.2) -9	6.76 10 -4	6.65 10 -5
	RDS (5.3) -11	7.70 10 -4	6.87 10 -5
	RDS (2.4) -7	5.41 10 -4	6.78 10 -5
	RDS (3.4) -9	1.63 10 -4	7.02 10 -5
	RDS (2.5) -5	7.05 10 -4	6.56 10 -5
	RDS (3.5) -7	7.54 10 -4	6.36 10 -5
	RDS (5.5) -6	1.27 10 -4	1.07 10 -4

Table 7 .

 7 A summary of both initial parameters and optimized values obtained for the individual kinetic and thermodynamic parameters necessary to calculate the NO to NO2 oxidation rate when considering RDS (3.5) as the best hypothesis.

	Reaction rate parameters
		K3 KRNO PO2	KRNO PO2	K ads NO	LFe
	for RDS (3.5)
	Parameters chosen for optimization	A3 B1 PO2 / mmol.h -1	E a RDS + ∆HRNO / kJ.mol -1	B1 PO2	∆HRNO / kJ.mol -1	B2 / atm -1	∆Hads NO kJ.mol -1 /	LFe / mg -1
	Estimated values	1.37 10 +3	44.0	3.70 10 +2	11.2	6.50	-20.0	0.3
	Kinetic and thermodynamic	A3 opt /	E a RDS /		∆HRNO /	B2 /	∆Hads NO	LFe opt /
	individual parameters	mmol.h -1	kJ.mol -1	B1 / atm -1	kJ.mol -1	atm -1	/ kJ.mol -1	mg -1
	Optimized values	9.23	33.7	2.03 10 +3	12.6	2.09 10 -1	-22.7	3.94

Acknowledgements

The financial support provided by UNICAEN is acknowledged.

6.

This work aimed at clarifying the NO to NO2 reaction mechanism over iron based zeolites. Due to the recent trend to develop SCR catalysts directly wash-coated onto the DPF monolith, highly hydrothermal resistant materials are under current development. For this reason, iron ferrierite was here considered as an interesting stable zeolitic structure and its ageing under hydrothermal conditions at 800°C was achieved to yield the FeFER800 catalyst.

The textural analysis evidenced that compared to the 'fresh' FeFER sample, FeFER800 presents both higher microporous and mesoporous volumes. This result is tentatively explained by an agglomerate dislocation phenomenon occurring under hydrothermal aging ('pine cone' opening) that would lead to a higher amount of isolated individual crystals. This phenomenon is 'by chance' in favor of a thorough kinetic study since the later requires working in the chemical regime for which internal and external mass transfer should not be limiting steps.

The absence of external diffusion limitation with FeFER800 was checked with a dedicated experiment while internal diffusion limitation was assumed minimum from comparison with literature data.

After, these preliminary verifications, a detailed mechanistic study was undertaken through a kinetic approach involving both catalyst data (operando) and gas phase data. Five distinct hypothetical mechanisms were considered with each of their individual step being considered as possible rate determining ones. A set of more than one hundred equations was obtained and a first data processing consisting in a linearization of reaction rates provided six distinct plots when operando data were used (iron mononitrosyls [*Fe_NO] were considered as the Most Abundant Reaction Intermediate) and five distinct plots when gas phase data were used (PNO). Some plots could easily be rejected due to a strong disagreement between experimental data and theoretical ones. On another hand, most of them could reasonably be further considered when looking at the determination coefficient R 2 as the only parameter. A next approach thus consisted in the direct calculation of reaction rate at a given temperature as a function of experimental variables and estimated values for constants (from preliminary linearization work) and their further optimization through minimization of the Standard Deviation (SD) using nonlinear optimization methods. Some other plots leading to the higher SD values were then rejected. At this step of the study, nine among nineteen distinct RDS (i.j) still remained as good candidates. Aiming at identifying the best one, the final approach consisted, for each remaining possible RDS (i.j), in processing simultaneously both the whole data (operando + gas) and the whole temperatures. Taking into account the resulting SD values after optimization and making a further look at the operando data with a focus on the semi-quantitative evolution of possible adsorbed NO2 species, finally allowed the best hypothetical reaction mechanism and its associated RDS to be identified. The best mechanism determined in the frame of this study thus involves isolated iron sites onto which NO and O2 co-adsorb and the corresponding rate determining step consists in the dissociation of the soformed Fe_NOO2 intermediate species. Activation energy and reaction enthalpy values were then obtained. Both the mechanism, among five independent ones and its RDS perfectly match with a preliminary work based only on theoretical considerations [START_REF] Brüggemann | Theoretical investigation of the mechanism of the oxidation of nitrogen oxide on iron-form zeolites in the presence of water[END_REF]. To the best of our knowledge, this is the first time that such an experimental work


Alexiane Luc
email: alexiane.luc@gmail.com<mailto

Sébastien Lê

Mathilde Philippe

Sebastien Lê

Nudging consumers for relevant data using Free JAR profiling: An application to product development

Keywords: Product development, Nudge, Free JAR, Data consistency, Sentiment score

INTRODUCTION

During the last two decades, the role of the consumer has drastically changed in the process of product development and product innovation.

Initially limited to hedonic assessments, consumers were then asked to provide their own sensory perception of the products. This sensory perception has moved from a very formatted perception, based on a list of descriptors a priori, to a freer perception, as consumers now provide a sensory description based on their own criteria. We have moved from a classic consumer profile to a rather holistic sensory profile, particularly achievable through a sorting step.

In order to get as close as possible to the consumer's thoughts, another strategy was to use the consumer's natural language: the rationale behind is that the less consumers are solicited, the closer the collected data will be to their real thoughts. In the same way, strategies that aim to decode body language, facial language, emotional and eye-tracking measures have also been used.

Nowadays, the question is no longer to integrate the consumer in the product development process, as we have already understood that consumers need to be integrated, but to know how to integrate them in the most efficient possible way. Whereas formatted measures can be easily analysed but can also be far from the consumers, measures that seem to be closer to the consumers are often very difficult to analyse and to interpret. A trade-off has to be found, in order to get data that are at the same time as close as possible to the consumer's mind, relatively easy to handle, and relevant for the ones who develop new products.

In this article, we propose an innovative strategy for providing such data, based on the nudge theory [START_REF] Thaler | Nudge: Improving Decisions about Health, Wealth, and Happiness[END_REF]: a friendly push to encourage a desired behaviour in a simple, costless and non-coercive way. Nudging is widely used to stimulate healthy behaviours as hand hygiene [START_REF] Caris | Nudging to Improve Hand Hygiene[END_REF], smoking cessation [START_REF] Sunstein | Nudging Smokers[END_REF], or reduction of energy consumption [START_REF] Allcott | Social Norms and Energy Conservation[END_REF][START_REF] Allcott | Behavior and Energy Policy[END_REF][START_REF] Allcott | The Short-Run and Long-Run Effects of Behavioral Interventions: Experimental Evidence from Energy Conservation[END_REF][START_REF] Costa | ENERGY CONSERVATION "NUDGES" AND ENVIRONMENTALIST IDEOLOGY: EVIDENCE FROM A RANDOMIZED RESIDENTIAL ELECTRICITY FIELD EXPERIMENT: Energy Conservation "Nudges" and Environmentalist Ideology[END_REF][START_REF] Momsen | From Intention to Action: Can Nudges Help Consumers to Choose Renewable Energy?[END_REF]. For example, Thaler and Sustein highlight that a nudge can make people reduce their use of energy, in peak period, by 40%. A little ball that glows red when a customer is using lots of energy, but green when energy consumption is modest was implemented. It plays the role of a nudge as it unconsciously encourages people not to want the ball to be red. Without the nudge, the energy consumption is 100 units whereas, thanks to the nudge, the energy consumption is 60 units [START_REF] Thaler | Nudge: Improving Decisions about Health, Wealth, and Happiness[END_REF].

Thus, it's demonstrated that nudges have an impact on people's behaviours. But a question appears: can they be used in order to impact people's speeches?

In fact, regarding our issues, we are convinced that a nudge can influence people to the desired speech. We aim to have access to a nudged textual data that present an added-value compared to a non-nudged textual data, by providing relevant, reliable and exploitable results in a product development context. By exploitable and reliable textual data, we mean textual data that highlight product improvement keys.

This nudging may emerge from two strategies' state of minds that are already developed.

One of the developed strategies is free comments data recording, developed in order to let the consumer free during their product assessment, without any constraints and with their own vocabulary. The state of mind of this strategy is to give strength and value to the spontaneity of the consumer. However, the fact is that today, the unconstraint assessment via free comments isn't satisfactory because it provides low quality data, which aren't directly usable in a product development context. In fact, in this context, the main idea is to provide product improvement keys, whereas free comment doesn't allow us to obtain this kind of data. When consumers are asked to answer the question "Why don't you like this product?", we notice that it is often difficult for them to express themselves accurately and in an operational way [START_REF] Lawless | Sensory Evaluation of Food[END_REF][START_REF] Symoneaux | Comment Analysis of Consumer's Likes and Dislikes as an Alternative Tool to Preference Mapping. A Case Study on Apples[END_REF]. Moreover, the analysis and the interpretation of data coming from this method could be complex and time consuming [START_REF] Lawrence | Using the Free Comments Method for Sensory Characterisation of Cabernet Franc Wines: Comparison with Classical Profiling in a Professional Context[END_REF]. Free comments are often use in order to describe products, but to our knowledge, the reflexion of using these descriptions in a product development context has never been done.

Another strategy is the JAR (Just About Right) method. JAR scales measure the appropriateness of the level of a specific attribute, and are used to determine the optimum levels of attributes in a product: they are widely used in food industry for product development as it mix hedonic assessment and sensory attributes [START_REF] Rothman | Just-About-Right[END_REF]. In practice, panellists evaluate a list of predefined attributes and have to say whether an attribute is too intense, just about right (JAR) or not intense enough [START_REF] Popper | Use of Just-About-Right Scales in Consumer Research[END_REF]. This method makes it possible to judge the intensity perceived in a product relative to the desired intensity. The state of mind of this strategy is to provide product improvement keys in a precise and structured way. Nevertheless, this method has some limits and doesn't seem to reflect the reality, due to the predefined list of attributes. This predefined list may be seen as a limitation of the method as it makes these attributes especially salient in consumer's mind, which may represent a bias as it can modify their ideal perception of the product [START_REF] Ares | Hedonic Product Optimisation: CATA Questions as Alternatives to JAR Scales[END_REF][START_REF] Epler | HEDONIC SCALES ARE A BETTER PREDICTOR THAN JUST-ABOUT-RIGHT SCALES OF OPTIMAL SWEETNESS IN LEMONADE[END_REF][START_REF] Popper | The Effect of Attribute Questions on Overall Liking Ratings[END_REF] or drive them to err. Indeed, they would be able to imagine sensory perceptions that do not objectively exist in the product [START_REF] Lawrence | Using the Free Comments Method for Sensory Characterisation of Cabernet Franc Wines: Comparison with Classical Profiling in a Professional Context[END_REF]).

In the same way, some major attributes, unperceived by the project leader but significant for the consumers, may be missing. Thus, it severely restricts the consumers because they don't express themselves according to their own sensory attributes and, in a product development context, this information is precisely the one that is relevant. On the other hand, using a predefined list can be useful as it can remind consumers of attributes they might overlook, but it also means taking the risk of emphasize attributes that are, in fine, not important for consumers. In fact, when consumers freely express themselves, they evaluate the product only according to the sensory descriptors they consider important and salient. This makes it possible to highlight the relative importance of the different descriptors in the perception of products.

These two methods are valuable and we aim to combine their state of mind in order to have access to a nudge strategy: the spontaneity strength of the free comments and the structure and R&D approach of the JAR. This new method will take into account the respective advantages of those two developed methods while avoiding their respective faults. Let's think about the interaction between the subject and the stimulus: in free comments, the subject is leading while in JAR, this is the stimulus. Our objective is to have access to a textual data balanced between the subject and the stimulus. Therefore, the aim of the present work is to design a new analysis strategy which unconsciously influences the consumers to be free during their product assessment while having an oriented and structured speech: it seems reliable to unlock consumer truth and identify product improvement keys. Beyond the protocol, it is also necessary to test the potential of this new analysis strategy and check the quality of the resulting data.

In this context, a new method called "Free JAR Profiling" was proposed to provide nudged textual data.

MATERIALS AND METHODS

2.1.

Free JAR Profiling protocol

Protocol

This new developed strategy allows panellists to evaluate a set of products according to their own vocabulary, but based on a JAR scale. The main idea behind is to allow consumers to use their own words, but with a constraint on how they give their opinion. Constraint consumers' speech via a JAR scale highlights faults and qualities of each product according to a consumer point of view, linking sensory descriptors and hedonic assessment.

Free JAR is a two-step-methodology, which is based on the nudge theory:

 The first step is a classification step: after discovering the whole product space, consumers have to classify products into 3 hedonic categories: "I don't like it", "I like it a bit" and "I like it a lot". This graduation may be thinner by including intermediate categories, but a threepoint hedonic scale may be acceptable in our case as we only want to place consumers in a hedonic state of mind. Thanks to this classification, we can impact consumers' speeches in a soft way: it allows them not only to be in a hedonic state of mind, but essentially to have a global vision of the product space and to structure their thoughts in this way: they unconsciously highlight product's qualities (if the product was placed in the "I like it a lot" hedonic category) and product's faults (if the product was placed in the "I don't like it" hedonic category). The knowledge of the products' characteristics in relation to each other feed the descriptions and make them richer than free comments.

 Then, once each product is classified, consumers have to describe them using their own descriptors according to a JAR syntax, as explained above: this is the second step of the methodology. Some examples are given to lead consumers to the right expression (Fig. 1).

In order to validate the protocol, an opinion poll was distributed to consumers who took part of the study to collect their assessment regarding the use of the Free JAR: was it easy to follow? Was it intuitive? Was it enough to describe products?

Delivered datasets

This new methodology conducts to a free and channelled expression, providing us specifically structured datasets. In order to validate our protocol and the resulting data, and to make sure that this new strategy brings an added-value compared to other strategies, we performed two Free JAR tests that allowed us to obtain two different datasets, structured in the same way. The first one, carried out in 2017, was used as a baseline to check the relevance of the implemented nudge, and to carry out a qualitative validation of the data obtained with our new methodology. This first data we recorded deals with perfume data: 15 perfumes were assessed by 93 consumers. The resulting dataset consists of 1395 rows and 4 columns. An extract is presented in Fig. 2.

The second one was the subject of a data collection realised in 2018, regarding car seat leatherettes: 10 samples of car seat leatherettes were assessed by 60 consumers. We provided a resulting dataset with 600 rows and 4 columns. An extract is presented in Fig. 3. It allowed us to check the consistency of the Free JAR data. The added-value of the Free JAR data

The relevance of the Free JAR data compared to free comments

As a reminder, each product is placed into one of the three hedonic categories. Following this ranking, the consumer is invited to describe these products with their own vocabulary, but according to a JAR scale. In order to validate the data quality of the recorded Free JAR data, we use data collected in 2017, regarding perfumes.

Firstly, in practice, we want to make sure that the new implemented method brings a real added value compared to free comments. To achieve this, the idea is to compare these two types of data recording and to study the provided words used to describe the products:  On the one hand, 93 people were invited to follow the Free JAR protocol in order to provide Free JAR data  On the other hand, 142 other people, with a similar profile to people who followed the Free JAR protocol, were invited to follow the free comment protocol. Each consumer evaluated 7 of the 15 perfumes. First, they were asked to evaluate each perfume following a 10-points liking scale. Then, two questions were asked regarding what they liked and disliked about each product: "What do you like about this perfume and why?" and "What do you dislike about this perfume and why?". A word classification is carried out in order to highlight the different type of words present in both datasets. The person in charge of the analysis realises this classification in regards of the words' meaning and it provides different semantic fields. We separate in priority useful words in a product development context, which means sensory attributes and hedonic assessments, from semantic fields unused in a product development context. For example, when dealing with perfumes, "strong" and "sweet" are usable words whereas "pleasant" doesn't highlight product improvement key, and is thus unusable in a product development context. The aim of the Free JAR data recording is to highlight product improvement keys, that means words which highlight products' qualities and faults. These kinds of words are usually sensory descriptors linked to hedonic assessments. It is therefore necessary to cluster the different types of words used to describe products in both methods as semantic fields, and then to see to what extent Free JAR data recording makes it possible to influence the consumers' speech towards usable data in an R&D context.

On the other hand, checking the relevance of these data from a qualitative point of view means checking the consistency between a set of words and a hedonic category. Indeed, as each product is first classified in a hedonic way and then described, it is necessary that words used to describe products placed in each hedonic category reflect the reality of the category: words used to describe products placed in the "I like it a lot" hedonic category must highlight qualities whereas words used to describe products placed in the "I don't like it" hedonic category must highlight faults. Revealing this kind of link will allow to say to what extent Free JAR data is more operational than free comments.

The consistency of the Free JAR data

Checking the consistency of the Free JAR data can be done by converting the textual data into a quantitative data, which would represent the consumer's speech as accurately as possible. Then, a way to achieve this is to call on sentiment analysis, and especially on sentiment score.

The goal of sentiment analysis, also known as opinion mining, is to evaluate the emotional tone related to a sentence [START_REF] Boullier | Chapitre 5. Détecter les tonalités : opinion mining et sentiment analysis[END_REF]. This tone can be represented by a number that we called "sentiment score". When the emotional tone induce by a sentence is positive (respectively negative), the sentiment score related to this sentence will be positive (respectively negative).

To calculate the sentiment score, we use a lexical approach based on dictionaries and weights assigned to each word and grammatical rule, which appears to be the most natural calculation method. In fact, as it is our first attempt with Free JAR data, we want to be in a controlling position, to be close to the data and close to the meaning we give them. This strategy is in line with the semantic approach we previously used to classify words in 2.2.1.

To achieve this, we firstly need to study the structure of sentences present in the dataset. As a reminder, we use the dataset that deals with car seat leatherettes to assess it. Each sentence is built with one polarized word, which is often the interest sensory descriptor, and with a cluster, which represents the surrounding word group of the polarized word, as a context. An example is displayed below:

"I REALLY LIKE THIS PRODUCT BECAUSE IT IS VERY ELEGANT"

Different packages allow to calculate the sentiment score on the R software: hunspell (Ooms et details 2017), spelling [START_REF] Ooms | spelling: Tools for Spell Checking in R (version 1.2)[END_REF] and sentimentr [START_REF] Rinker | Dictionary based sentiment analysis that considers valence shifters: trinker/sentimentr[END_REF] 2018) are the main used packages. The three of them are based on weights and dictionaries, but spelling isn't able to propose suggestions of correction and only one of them can store modifications and add other words to its dictionary: the sentimentr package. This is the one we chose to use. This package allows to quickly calculate the sentimental polarity, at a sentence level. Each polarized word (also denoted as pw) is weighted, firstly by its own weight, and then by the weight of the different types of words present in the surrounding group.

In practice, to calculate the sentiment score, we firstly need to have access to two dictionaries, as Tyler Rinker explains in his package instruction manual [START_REF] Rinker | Dictionary based sentiment analysis that considers valence shifters: trinker/sentimentr[END_REF] 2018):

 a polarity dictionary which assigns a positive, neutral or negative nature to each word, tagged with a +1, 0 or -1 respectively.  a valency dictionary which assigns to each type of words present in the surrounding group its nature: negator, amplifiers, de-amplifiers or adversative conjunctions. We can create our own dictionaries or choose ones that are already filled: we created our own dictionaries for this study, specific to perfumes and car seat leatherettes, which suit as accurately as possible our datasets.

Then, the software checks automatically that each word is present in the polarity dictionary. A group of words, allowing to determine the context of the sentence is thus selected: it corresponds to 4 words before the polarized word and 2 words after. These are default values but the user can choose their own numbers of word to keep before and after the polarized word. Thus, the considered group of word, that we called cluster, is define as: C = {pw -4, …, pw, …, pw+2} where pw represents the polarized word The different types of words present in the cluster impact in different ways the polarized word during the calculation:

 Neutral word: the equation doesn't take into account this type of word but it affects the number of words present in the cluster.  Amplifier: increases the impact of the polarized word (ex: I really like it). It multiplies the polarity of the polarized word by 1 + 0.8. This is a default value, but the user can choose their own amplifier weight. This value must be between 0 and 1, and will multiply the polarized word by 1 + the chosen value.

It becomes a de-amplifier if the cluster contains an odd number of negators, and aims to decrease the polarity (ex: I hardly like it).  Negator: flips the sign of the polarized word (ex: I don't like it). Negation is determined by raising -1 to the power of the number of negators present in the cluster. This provides the sign of the polarized word. It also acts on amplifiers / de-amplifiers as explained above.  Adversative conjunction: overrules the previous clause containing the polarized word (ex: I like it but it's not worth it). When it's placed before the polarized word, it multiplies the number of words placed before the polarized word in the cluster by 1*0.85 and then adds 1. When it's placed after the polarized word, it multiplies the number of words placed after the polarized word in the cluster by -1 * 0.85 and then adds 1. This calculation method is based on the belief that an adversative conjunction increases the weight value of the next clause while lowering the weight value of the previous one [START_REF] Rinker | Dictionary based sentiment analysis that considers valence shifters: trinker/sentimentr[END_REF] 2018). The weight 0.85 is a default value, but the user can choose their own weight for adversative conjunctions.

Thus, sentences containing these different types of words will lead to different sentiment scores:

 "I really like this product because it is very elegant"  0.67  "I don't like this leatherette because it's too fluffy"  -0.34  "I like this product even though it seems a little bit cheap"  0.29

All these calculations provide a sentiment score for each sentence. Therefore, we have access to a fifth column in our dataset, which allows to check the consistency of Free JAR data. Our resulting dataset is presented in Fig. 4.

In order to check the consistency of Free JAR data and given our dataset, analyses of variance are carried out. In fact, we can say that a judge is qualified as consistent if the way he perceives the product in Free JAR description is consistent with the way he ranks the product. Thus, we want to check a consistency between a group of words and a hedonic category. As we have already transformed these groups of words from Free JAR method into a numerical one via sentiment analysis, we can use the sentiment score previously calculated to realise this quantitative data checking.

Thus, we can affirm that a consumer is consistent if the sentiment score obtained for a given product matches with the hedonic category in which the product was placed in. An analysis of variance may be used to study the relationship between the sentiment score and the hedonic category. Indeed, analysis of variance is used in order to study the behaviour of a quantitative variable (the sentiment score in our case) explained as a function of one or more categorical variables (the hedonic categories in our case). This relationship study will allow to see to what extent the developed method provides oriented textual data, that are consistent with the hedonic category in which the product has been placed.

Drivers of liking

The study of the different words used in consumers' speeches in order to describe products allow us to highlight the drivers of liking and disliking related to each product. Indeed, highlighting words significantly more used to describe a product than the others related to the sentiment score associated with this product is a strategic tool regarding the outcome of the study. In fact, it allows to see which particular feature provides a better or a lower sentiment score for a product, compared to other features.

To highlight these drivers of liking or disliking, we carried out a description of frequencies. A word is considered as a driver of liking or disliking if its abundance in the class is considered significantly higher than what we can expect given its presence in the population. We note:

-Nkj the number of times the interest word j has been cited to describe the product k among all the words Nk cited to describe the product k -Nj the number of times the interest word j has been cited to describe all the products among all the words N cited to describe all the products The abundance of the interest word j is defined by comparing its percentage in the k th class with its percentage among all the products. We define:

-H0: when the Nk words used to describe the product k are randomly selected without putting them back among the N words used to described all the products, the percentage of the interest word used to describe the product k and the percentage of the interest word used to describe all the products coincide at: Then, a test corresponding to the hypergeometric distribution is performed and the probability to observe a more extreme value than the one observed is calculated [START_REF] Lebart | Statistique exploratoire multidimensionnelle[END_REF][START_REF] Husson | FactoMineR: Multivariate Exploratory Data Analysis and Data Mining (version 1.41[END_REF].

Data visualisation: the "Sentiment Mapping"

Once the consistency between the sentiment score and the hedonic assessment of the product is checked, it seems reliable to take advantage of this score to obtain an intuitive and ergonomic data visualisation of the results.

To achieve this, we carried out a Multiple Factor Analysis (MFA) on the dataset presented in Fig. 5, which comes from the 2018 dataset, dealing with car seat leatherettes. This dataset represents two combined table. The first one represents the hedonic category in which each product was placed in by each judge. The second one is a contingency table between the products and the hedonic categories. This analysis aims to highlight and study the similarities between products from the point of view of all variables (François [START_REF] Husson | Exploratory multivariate analysis by example using R[END_REF]. We interpret MFA's results as follows: two products are even closer as they have been placed a large number of times in the same hedonic category at the panel level [START_REF] Brard | Adaptation of the Q-Methodology for the Characterization of a Complex Concept through a Set of Products: From the Collection of the Data to Their Analysis[END_REF].

As in an external preference mapping (François Husson, s. d.), the sentiment score replaces consumers' preferences in order to project on the product space a response surface indicating a proportion of consumers having a good sentiment of the product. This good sentiment represents the mean of the sentiment scores calculated for each product. Then, remarkable drivers of liking or disliking previously highlighted are displayed, allowing a direct interpretation of the map. This produced map is called "Sentiment Mapping".

RESULTS

In order to validate the consistency and the reliability of the new developed method, which allows us to highlight structured textual data, oriented towards product improvement keys, we must first validate our protocol from a user's point of view and then check the relevance of the provided data. On the one hand, it is necessary that the user does not have any problems with the protocol, which has to be easy and intuitive to follow. On the other hand, it is necessary that this developed data recording provides high quality data and makes it possible to meet the objectives previously set.

Protocol validation from a user's point of view

Thanks to our first data recording trial, dealing with perfume data, we attempted to validate the protocol of our new method. To achieve this, an opinion poll was distributed to consumers who took part of the study. It turns out that 81% of the consumers found the Free JAR useful, 80% managed to use the Free JAR and 77% found the Free JAR enough to describe the products. Thus, the protocol of our new data recording seems intuitive and easy to follow for users. It seems reasonable to say that it would be adapted as a potential routine development.

3.2.

Highlighting the added-value of the Free JAR data 3.2.1. Checking the relevance of the Free JAR data compared to free comment Firstly, in order to make sure that the new implemented method brings a real added value compared to free comments, we realised a graph as presented in Fig. 6. The overview of the words present in the dataset allows us to realise a sorting of them according to 7 semantic fields: sensory descriptors, intensity, concept, memory, appreciation, sense and context. We sorted all the words used in both method and it provides the presented graph. It represents the number of times the different semantic fields are used to describe products in both methods. First of all, we notice that free comments use more diversified type of words than the Free JAR data recording. In fact, words linked to appreciation, context, memory and sense are much more used to describe products in free comments. On the contrary, we note that sensory descriptors or type of words linked to the intensity are much more used to describe products during the Free JAR data recording: the Free JAR strategy uses less words, but they are more usable in a product development context.

Thus, in the light of the kind of data we want to obtain, the Free JAR method seems to be able to answer our objectives. In fact, although free comments provide diversified type of words, these textual data are less usable in a product development context, where the goal is to highlight sensory descriptors that allow to define products' qualities and faults. On the contrary, Free JAR data recording, that uses numerous sensory and intensity descriptors, provides more usable data which highlight product improvement keys: consumers are implicitly led to structure their speech towards sensory descriptors. Free JAR data are, in this way, more relevant in a qualitative point of view.

On the other hand, in order to check the relevance of the Free JAR data from a qualitative point of view, we realised the graph presented in Fig. 7. To answer the objectives previously stated, this graph represents the number of times the terms "Just about right", "Not enough", "Too much" and descriptive words have been used to describe products placed in the 3 different hedonic categories: "I don't like it", "I like it a bit" and "I like it a lot".

We notice in the resulting figure that "Not enough" and "Too much" terms are more used to describe products placed in the "I don't like it" hedonic category than to describe products placed in the "I like it a lot" hedonic category. In the same way, we notice that "Just about right" term is more used to describe products placed in the "I like it a lot" hedonic category than to describe products placed in the "I don't like it" or "I like it a bit" hedonic category. Thus, each hedonic category is characterized by its own words, highlighting faults for the "I don't like it" hedonic category and qualities for the "I like it a lot" hedonic category. We can therefore affirm that the dataset quality is checked from a qualitative point of view.

In order to confirm this structured distribution, we realised Chi2 tests on contingency tables, which compared the expected distribution versus the real distribution. It confirms our thoughts: words are significantly structured through the hedonic categories with a p-value lower than 2e-16.

Checking the consistency of the Free JAR textual data

In order to check the Free JAR data quality in a quantitative way using the new numerical data previously calculated (the sentiment score), as many analyses of variance are performed as there judges in the dataset. Given a judge and thanks to the analysis of variance, we have access to the mean of the sentiment score for each hedonic category. Provided results highlight different types of judges:

 Perfectly consistent judges in a sentiment score point of view: the mean of the sentiment score for the "I like it a lot" hedonic category is higher than the one for the "I like it a bit" hedonic category, which is higher than the one for the "I don't like it" hedonic category.  Moderately consistent judges in a sentiment score point of view: the mean of the sentiment score for the "I like it a bit" hedonic category is higher than the one for the "I like it a lot" hedonic category, or lower than the one for the "I don't like it" hedonic category.  Inconsistent judges in a sentiment score point of view: the mean of the sentiment score for the "I like it a lot" hedonic category is lower than the one for the "I don't like it" hedonic category. As an example, Table 1 presents the result of the analysis of variance for a perfectly consistent judge in a sentiment score point of view.

Analyses of variance are realised for each judge present in our dataset that deals with car seat leatherettes. They highlight that 56% of the judges are perfectly consistent while 44% of the judges are moderately consistent. In this dataset, we didn't find any inconsistent judges and we therefore didn't remove any of them from the dataset. This allows us to proceed further with the analysis.

Provided graphic representation

Once the dataset is filled, the sentiment score is used in order to perform the "Sentiment Mapping". This representation is presented in Fig. 8. Products are represented by letters. Those present in the red area are products that drive a bad opinion, whereas those present in the green area are products that drive a good opinion. Thus, we can notice that products J, C and F generate a better opinion than products G or D. Drivers of liking and disliking projected allow us to say that product G doesn't seem rigid enough while product D seems too fluffy to consumers.

CONCLUSION AND DISCUSSION

As a conclusion, we provide today a new way to collect data for market research institutes based on the nudge theory, which lead consumers to the desired speech, highlighting product improvement keys, essential in a product development context. This information can be summed up into an ergonomic and intuitive map: the "Sentiment Mapping". This new representation puts the consumer at the heart of the process, as expected. In fact, data are only based on consumer speech and the provided map allows an easy access to the faults and qualities that each of the tested products may have. Moreover, it positions products against each other regarding their sentiment score. The developed method lets the consumers freely express themselves, while structuring their thoughts in order to influence their speech toward products' faults and qualities.

However, we can highlight some limits and discussion points regarding the new developed method.

First, regarding the first step of the Free JAR method, a discussion must be done with the client in order to define the labels of the different hedonic categories ("I like it a lot", "I like it a bit", "I don't like it"). Indeed, these labels can influence the representation consumers have regarding the different categories. Moreover, we agree that there may have a potential loss in sensitivity by using a simple three-point hedonic scale and a discussion can be held regarding the different strategies we can set up in order to put consumers in a hedonic state of mind.

Then, the classification of the words used for the qualitative validation of Free JAR data is quite subjective. Indeed, the person in charge of the analysis has to class words according to their perception: it seems unlikely that two people performing this task independently will result the same words' classification. It would be necessary to drive the study further in order to highlight salient and optimal categories, differentiating usable words in a product development context from unusable words in a product development context, and bringing together all types of words present in the dataset. Machine learning strategies could be considered [START_REF] Pradhan | Support Vector Learning for Semantic Argument Classification[END_REF].

Regarding the calculation of the sentiment score, we use today a lexical approach, as it is previously explained. But since the relevance and the interest of the nudge has been demonstrated, we can think about machine learning strategy (Hatzivassiloglou et McKeown, s. d.). This strategy aims to train the software to detect expressions, models, patterns via a first test corpus in order to be able to detect these models in the corpus of interest, or even to detect new ones, close to those it already knows. The main interest of this strategy is that it will allow us to move away from dictionaries, which are time-consuming to set up, specific for each product space and which are not specially filled in an objective way, as they are filled according to our perception.

Then, we wanted to discuss more the concept of "consistency" for one consumer. As we defined the concept of consistency with Thierry Worch in our paper [START_REF] Worch | Assessment of the Consistency of Ideal Profiles According to Non-Ideal Data for IPM[END_REF], we defined the concept of consistency in the Free JAR context by answering two major questions:

(1) Are the descriptions in agreement with the hedonic classifications? (2) Have the products placed in the "I like it a lot" category a better sentiment score than the others? More generally, consistency is defined as the fact that a consumer follows the same direction from one task to another. However, we are conscious that people can find drawbacks for a product, even if they like it a lot: that's why we keep the moderately consistent judges for the analysis.

Thus, the fact that 44% of the consumers are "moderately consistent" for the quantitative validation of Free JAR data encourage us to go further regarding the understanding of these judges. Indeed, it is encouraging but it also means that there is still work to be done. In fact, we don't know well how to construe them and how optimize the analysis in order to make the calculation of the sentiment score more accurate: here again, machine learning strategies could be considered.

We compared in this manuscript Free JAR data with free comments. However, we didn't compare Free JAR data with classical JAR data. As we wanted to move away from constraints imposed by the JAR method, it seemed more natural for us to compare Free JAR data with free comments: we aimed to bring added-value to a low-quality data, providing an "oriented" free comment. But the comparison between Free JAR data and JAR data will be the subject of further works.

A discussion should also be hold regarding the size of the product space. Indeed, the Free JAR method aims to analyse large product spaces, thanks to appropriate multivariate analyses. However, when the product space is too small, the method must be reconsidered. In fact, we can still put consumers in a hedonic state of mind and make them express via the Free JAR method, but we are currently considering to what extent comparison between products can be identified as the MFA can't work with such a small number of products.

Finally, this new method highlights a new kind of data, a quantitative score built from textual data: the sentiment score. It helps to get as close as possible to the consumer by quantifying the feelings a consumer has about a product. Beyond the Free JAR method, the sentiment score allows us to think about other applications, in other contexts and fields.

This study is part of a Master's degree project, realised thanks to Agrocampus-Ouest. We want to thank Strategir, that gave us the opportunity to realise this project, that carried out the data recording and allows to go further in future years. A very special thanks to Laure Bonnet, Marie Boutigny, Sonia Guillou and Aubery Lebas for their previous work that helped us a lot. In the end, we particularly wanted to thank our best partners, Mathilde Doyen and Vanessa Morin. Acknowledgment is also expressed to the two reviewers for their insightful comments, as these comments helped us to significantly improve the manuscript.

 In a product development context, the nudge theory can be used in order to influence consumers' speeches toward product improvement keys  JAR and free comments data recording have limits in a product development context  The Free JAR strategy lets consumers freely express themselves while structuring their speech thanks to a nudge step  Sentiment analysis can be use in order to check the consistency of the Free JAR data  The "Sentiment Mapping" positions products against each other regarding their sentiment score in an intuitive and ergonomic way

Figure 1 :

 1 Figure 1: Summary figure of the Free JAR method protocol

Figure 2 :

 2 Figure 2: Extract of the perfume dataset

Figure 4 :

 4 Figure 4: Resulting dataset after the processing via sentiment analysis

Figure 5 :

 5 Figure 5: Dataset used in order to realise the MFA

Figure 6 :

 6 Figure 6: Number of times words relative to the different semantic fields are used to describe products regarding free comments and Free JAR data recording

Figure 7 :

 7 Figure 7: Number of times terms are used to describe products placed in the hedonic categories

Figure 8 :

 8 Figure 8: Sentiment Mapping provided thanks to the car seat leatherette dataset

Table 1 :

 1 Result of the analysis of variance for a perfectly consistent judge in a sentiment score point of view

	Ftest	F value	P-value
	Hedonic_category	5.1061	0.0429
	Hedonic category	Coefficient	P-value
	I like it a lot	0.80842	0.02675
	I like it a bit	-0.16120	0.55374
	I don't like it	-0.64722	0.02707

Acknowledgements