François Rohart

Sinda Mejri

Papa Lat

Tabara Sow

Sean K Tokunaga

Christian Chardonnet

Benoît Darquié

H Dinesan

E Fasci

A Castrillo

L Gianfrani

P L T Sow

C Daussy

Absorption line shape recovery beyond the detection bandwidth limit: application to the precision spectroscopic measurement of the Boltzmann constant

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

I. INTRODUCTION

Spectroscopy, the study of the interaction between radiated energy and matter, has played and is playing a crucial role in many domains of Science. One can think of the development of quantum physics and the study of atomic structure. In physical and analytical chemistry, atomic and molecular spectra are used to detect, identify and quantify key information. In astronomy spectra observed with telescopes are used to determine the chemical composition and physical properties of astronomical objects.

In recent years, there has been a growing interest in highly precise and accurate observations of the shape of molecular spectral lines. Climate modeling and global change research programs are setting unprecedented accuracy targets in gas-sensing missions for atmospheric CO 2 and other greenhouse gases [1]. The desired uncertainty can only be reached by making high quality measurements of spectroscopic parameters (including pressure broadening coefficients and line intensity factors) using well-designed and characterized experiments [2][3][4][5]. Similarly, the interpretation of spectra of astrophysical and planetary interest needs a precise knowledge of lineshape parametres and current databases require further improvements [6,7]. The accurate observation of line profiles is also crucial to the physics of collisions by testing theories modeling the shape of atomic or molecular transitions perturbed by collisions [8][9][10][11][START_REF] Hartmann | Collisional effects on molecular spectra[END_REF]. Highly accurate spectroscopy plays as well a decisive role in precision measurements devoted to metrological applications and tests of fundamental physics. Spectroscopy of constituant of atoms, atoms themselves, molecules, simple exotic atoms (anti-hydrogen, muonic atoms,…) is being used to test quantum electrodynamics, to test fundamental symetries (such as P, PT, CPT, matter/antimatter,…), to test postulates of quantum mechanics (symmetrization postulate, wavefunction collapse,…). It is being used also to measure fundamental constants and properties (fine structure constant, Rydberg constant, proton-to-electron mass ratio, Boltzmann constant,…) and their possible variation in time [START_REF] Mohr | [END_REF]14].

The present paper identifies a source of systematic effects that may have been underestimated so far: it investigates the possible inaccuracy in the experimental determination of line shape parameters -central frequency, various contributions to the line width, line intensity,…due to the unavoidably limited bandwidth of the detection chain with which spectra are recorded. To the best of our knowledge, the only published work addressing this particular issue regarding the detection bandwidth is Townes and Schawlow's book where they present a rule of thumb for circumventing it [START_REF] Townes | Microwave Spectroscopy[END_REF]. Given the unprecedented sensitivity and precision of recent spectrometers, a detailed study is becoming increasingly relevant. This is the case, for instance, of the 'fast-scan' technique where frequency varies rapidly [START_REF] De Piante | [END_REF]17].

The present study was initially motivated by ongoing experiments dedicated to Doppler Broadening Thermometry (DBT), a relatively new technique used in our laboratories to determine the Boltzmann constant (k B ) [START_REF]Experimental determination of Boltzmann's constant[END_REF][START_REF] Fischer | The IMERAPlus Joint Research Project For Determinations Of The Boltzmann Constant, Temperature: Its Measurement and Control in Science and Industry[END_REF]. DBT consists in retrieving the Doppler width from the accurate measurement of the linear absorption profile of an atomic or a molecular transition, in a gaseous sample at the thermodynamic equilibrium. A determination of k B by DBT with a combined uncertainty of 1 ppm, comparable to the best current uncertainty obtained using acoustic methods, would make a significant contribution to any new value of this constant determined by the Committee on Data for Science and Technology (CODATA). Furthermore, having multiple independent measurements at these accuracies opens the possibility of defining the kelvin by fixing k B , an exciting prospect considering the upcoming redefinition of the International System of Units (SI) [START_REF] Bipm | Resolutions adopted by the General Conference on Weights and Measures (24th meeting)[END_REF][START_REF] Fellmuth | [END_REF][22]. One important result of this work is to quantify the inaccuracy on the spectroscopic determination of k B due to the limited detection bandwidth. This paper begins by describing in Section II a model showing that a finite measurement bandwidth results in a distortion of the line shape accompanied by a shift of the retrieved central frequency. Section III validates this model by the analysis of high-quality linear absorption molecular spectra recorded in different spectral regions. Linear absorption is a particularly interesting and challenging case as it puts at stake complex profiles involving many inhomogeneous and homogeneous contributions to shifts, broadenings and narrowings of the line. Section IV describes possible means of recovering the original central frequency and line shape parameters. Finally section V discusses the implications of these effects for precision measurements of the Doppler width by DBT.

II. THEORETICAL MODEL

Two key cases are considered. First, we consider the effect of the detection bandwidth on the recorded absorption signal assuming a continuous sweep of the laser frequency. We then extend this treatment to a frequency sweep consisting of a serie of discrete steps, as is the case in most spectrometers.

A. Impact of the detection bandwidth on recorded absorption signals

Let us consider the case of an isolated line, the absorbance A() of which is small enough so that the Beer-Lambert law can be considered in its linear form (sample transmittance is given by

  1 A  
) 1 . In laser absorption spectroscopy, the absorbance A() is typically recorded as a function of the laser frequency  that evolves linearly with time t at a constant sweep speed dt d    (in Hz/s), assumed positive unless explicitly quoted. The detection chain can be viewed as a low-pass filter, generally of either the first or the second order with -6 or -12 dB/octave roll-off, respectively.

In case of the 2 nd order filter, frequently considered when using a lock-in detection, the time evolution of the recorded signal D(t) is given by [START_REF] Blinchikoff | Filtering in the time and frequency domains[END_REF]

2 2 2 () () ( ) ( ) D D d D t dD t D t A t dt Q dt      (1)
where  D is the filter time constant, Q the filter quality factor which is usually less than 1 for useful low-pass filters and A(t) is the time evolution of the absorbance A() under study.

Eq. ( 1) can be re-written in terms of laser frequency as

2 22 2 () () ( ) ( ) DD dD dD Q D A dd           (2)
where

Q D D     
is a "frequency constant", a characteristic parameter of experimental recording conditions, and D() is the signal recorded at the laser frequency .

In order to avoid unwanted signal deformations, the time constant  D , and therefore  D , has to be chosen to be small enough with respect to the time interval required to record the whole line profile [START_REF] Townes | Microwave Spectroscopy[END_REF]. In this case, by analogy with signal processing theory [START_REF] Blinchikoff | Filtering in the time and frequency domains[END_REF][START_REF] Papoulis | Signal analysis[END_REF], an approximated solution of Eq. ( 2) is a detected signal D() that reproduces the expected 1 In order to avoid any coherent transient problem due to rapid passage, which is beyond the scope of this paper [START_REF] Shoemaker | Laser and Coherence Spectroscopy[END_REF], collisional relaxation is assumed large enough so that A() actually corresponds to the steady state regime at the frequency . Modifications of the laser frequency at the scale of one relaxation time constant must be smaller than the collisional line width, i.e. In order to get a better insight into the actual recorded signal, a more accurate solution can be obtained from a development of D() in powers of  D and written as

1 ( ) ( ) ( ) . ( ) k D D k k DA             (3)
where  k () are trial functions and  

D A   can be expressed as a function of A() derivatives 1 ( ) ( ) ( ) ( ) . ! D D dA AA d             . ( 4
)
By using Eqs. ( 3) and ( 4) and comparing identical powers of  D , Eq. ( 2) leads to a set of coupled differential equations linking  k () functions and their 1 st and 2 nd derivatives to A()

derivatives. After simple calculations, one obtains:

23 2 2 2 3 23 ( ) ( ) ( ) ( ) (1/ 2 ).( ) .
(5 / 6 2 ).( ) . ...

D D D d A d A D A Q Q dd               . ( 5
)
To the lowest order, the recorded line is thus simply shifted (to higher or lower frequencies depending on whether the laser frequency is increasing or decreasing) without any deformation. It is worth noting that this shift, given by the frequency constant  D , is independent of the actual line shape. The second term depends on the second derivative of A(). In case of a symmetric line shape, this term reaches a negative minimum value at the line center frequency  0 and is nearly zero in the vicinity of the two frequencies corresponding to half maximum. This entails a reduction of the line amplitude and thus a modification of the line shape resulting in an asymmetry and a line width modification. However, it is interesting to note that this term vanishes for

1/ 2 Q 
, a condition which is fulfilled in the case of the so-called Butterworth filter [START_REF] Blinchikoff | Filtering in the time and frequency domains[END_REF]. Unfortunately, it seems that for many lock-in amplifiers [START_REF]Model SR830 DSP Lock-In Amplifier[END_REF], the -12dB/oct roll-off is obtained with two identical successive 1 st order filters, where 12 Q  instead. The third term depends on the third derivative of A(), an odd function when the line shape is symmetric. So this term contributes also to an apparent line shape asymmetry. Subsequent terms of Eq. ( 5) are generally small and contribute to more complex line shape distortions. In conclusion, in the case of a 2 nd order low pass filter, we expect an impact on the line width as well as a distorted line shape which leads to an apparent shift on the line center frequency. This description can be extended to the case of a 1 st order filter. It is easily shown that previous equations also hold by setting 0

Q  , except the frequency constant  D is given by     . D D 
, where  D is the 1 st order filter time constant.

B. Impact of the detection bandwidth on recorded dipole moment correlation function

By moving to the time domain by Fourier transform, the signal D() can be replaced by its Fourier transform

) ( ~ D :            d i D D . ) 2 exp( . ) ( ) ( ~. (6)
A similar equation holds for the Fourier transform of the absorbance A() which can be interpreted as proportional to the correlation function () of the dipole moment induced in the gaseous medium after a laser excitation starting at time  = 0 [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF][START_REF] Sobel | man, Introduction to the theory of atomic spectra[END_REF][START_REF] Rohart | [END_REF]. For the 2 nd order filter case, Eq. ( 2) becomes [START_REF] Blinchikoff | Filtering in the time and frequency domains[END_REF] 2 :

( ) ( ). ( )

DG     (7)
where ) ( ~ G can be seen as the complex linear "gain" of the system given by

2 ) 2 ( 2 1 1 ) ( ~       D D Q i G    . (8)
Eq. ( 7) tells us that the detection system properties can be taken into account by simply multiplying the correlation function (), by the gain

) ( ~ G
of the system, thus leading to the following expression:

() () 1 2 (2 )
DD D iQ            (9)
that can be included in the spectrometer instrumental function in the line shape modeling.

It is worth noting that this result is exact, quite an interesting property for fitting purposes by comparison with the frequency domain solution given by Eq. ( 5) development. Moreover, () has an analytical form for a number of line profiles such as Voigt, Galatry, Speed-Dependent Voigt and Speed-Dependent Galatry models [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF][START_REF] Rohart | [END_REF][29][30][31], including the case of frequency modulated spectral profiles [32]. Of course, the result is not restricted to the 2 nd order low pass filters (or to the 1 st order ones by setting Q = 0), and can be generalized to more complicated detection schemes.

Furthermore, this result can be extended to optically thick media for which the Beer-Lambert law cannot be replaced by its linear approximation. In this latter case, the sample transmittance T() will be given by     exp TA     and its Fourier transform ) ( ~  [33].

Then, the sample detected transmission will be proportional to the Fourier transform of

) ( . ) ( ~   G .

C. Application to the Voigt profile

As an illustrative example, let us consider the Voigt profile in more detail. The corresponding dipole correlation function is [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF]31] 2 0 ( ) exp 2 ( ) ( )

Voigt coll Dop i                 ( 10
)
where  0 is the line center frequency,  coll the collisional width (half width at half maximum, HWHM, of the Lorentzian contribution to the profile) and  Dop the Doppler width (halfwidth at 1/e of the maximum of the Gaussian contribution to the profile). By using the Taylor expansion of ln[ ( )] G  along with Eq. ( 10), the Fourier transform ()

Voigt D  of the detected signal D() becomes: 0 ( ) exp 2 ( ) Voigt D coll D i                                  ... ) 2 ( . ) 3 / 1 ( ) ( ) 4 2 ( 3 2 2 2 2 2        D D Dop Q i Q . ( 11
)
For small values of the time this asymptotic expansion in terms of  facilitates useful interpretations, while remaining in good agreement with results from Eq. ( 5).

The imaginary and real parts of the -term show that the absorption line center  0 is frequency shifted by  D whereas the collisional broadening  coll remains unaffected.

On the other hand, the  2 -term is responsible for a modification of the line shape, where the gaussian contribution Gauss   to the Voigt profile appears to be different from the pure Doppler width, according to the following expression:

2 2 2 ) 4 2 ( D Dop Gauss Q         . ( 12
)
Finally, the  3 -term is imaginary and thus leads to a line asymmetry. Note that the area of the recorded line remains unaffected since ( 0) ( 0) 1 D       [24].

At this point, it is useful to introduce some typical values and orders of magnitude to facilitate the discussion about the motivations of our work. Among spectroscopists, a rule of thumb is that the detection time constant  D should be at least 20 times smaller than the duration required for recording the line shape over one half-width [START_REF] Townes | Microwave Spectroscopy[END_REF], thereby constraining the detection frequency constant  D . For low pressure experiments, namely in the Doppler regime, this condition leads to order filter with 12 Q  . This means that the recorded line center will be shifted by about a tenth of the Doppler width, a value which could be far from being negligible considering the accuracy and signal-to-noise ratio achieved with modern laser-based spectrometers.

Under the same operation conditions, the apparent Doppler width will be slightly increased, by about 5 10 -3 . Such a value, actually negligible for common spectroscopic studies, must be considered very carefully in case of the experiments to measure the Boltzmann constant via the Doppler width [34][35][36], where a 1ppm combined uncertainty is being targeted. In the case of a 2 nd order filter with the usual quality factor 12 Q  [START_REF]Model SR830 DSP Lock-In Amplifier[END_REF], this requirement leads to a D Dop   ratio as small as 1/700 that requires a very small  D time constant and/or low frequency speed  . In this respect, it is worth noting the advantage of implementing a 2 nd order Butterworth filter in a lock-in amplifier: its specific Q-value ( 2 / 1 ) leads to 1 st order to a gaussian width which is unaffected by the value of the frequency constant  D and equal to the Doppler width  Dop (see Eq. 12).

Note in passing that the theoretical model proposed here can also be applied to line shapes relevant for sub-Doppler (saturated or two-photon absorption) spectroscopy widely used in frequency metrology and high-resolution spectroscopy of molecules, atoms or ions. In these cases, only the homogeneous (Lorentzian) profile needs to be considered.

D. Step-by-step frequency sweeping mode analysis

So far, we have considered a continuous tuning of the laser frequency. However, for many spectrometers, typical experimental conditions correspond to a frequency  swept stepby-step via a frequency synthesizer, each frequency step  having a time-duration t , thus leading to an average frequency sweep speed given by t      . As the laser frequency changes, taking the value  n at time t n , the sample absorbance

A(t) should consist of a sequence of steps, each of them being     n A t A  
for nn t t t t     . After detection, A(t) is treated by the amplifier acting as a low pass filter (Eq. 1), leading to the signal D(t) which is sampled at time t n + t (just before a new frequency change), the delay t allowing for filter integration. This step-by-step frequency sweeping and sampling mode was modeled by numerically integrating of Eq. ( 2). This allowed artificial line shapes D() to be generated. For simplicity, the gas absorbance A() was taken to be a gaussian line shape. In order to measure the distortion caused by the detection system, the 'distorted' D() line shapes were fitted using a gaussian profile. The fit parameters, the central frequency  fit , the gaussian width  Gauss and the line amplitude, were then compared to their 'true' values with which the original A() profile was generated. ) and it is found that the frequency deviations can be written as:

0 . fit D a      , (13)
Where a  is a parameter depending on the considered filter (1 st order, 2 nd order with

12 Q  or 12 Q 
) and on  D /t ratio. Corresponding a  -values are collected in TABLE I. Limiting cases are easily understood, a  tending towards zero for small  D /t values and towards 1 for large  D /t values. This latter case corresponds to the continuous frequency sweeping operation model which always represents an upper limit for the frequency deviations (see FIG. 1, thick line). The frequency deviation increases with  D , whatever the value of  D /t ratio is, and for a given frequency step value , the smaller is  D /t the smaller are the frequency deviations. This means that, for each t, a sufficient time interval is left for a perfect signal integration before sampling.

Since for the width, the effects of having a step-by-step spectrometer operation are more complicated, corresponding discussion is postponed to section V.

III. DESIGN FEATURES OF EXPERIMENTAL SETUPS

A. Laser Physics Laboratory spectrometer

A set of experiments were done on the saQ(6,3) rovibrational line of the  2 vibrational mode of 14 with the LPL's spectrometer operating in the 10 µm range, detailed elsewhere [37,38]. We simply recall that the frequency was controlled step-by-step and that the signal was amplitude modulated at 40 kHz via a microwave-infrared frequency mixer and demodulated by a lock-in amplifier (Stanford Research model SR-830) operating in the -12 dB/oct roll-off mode (note that for the current study, line shape broadening due to amplitude modulation is negligible [35]). As explained in Ref. [START_REF]Model SR830 DSP Lock-In Amplifier[END_REF], the lock-in amplifier output is a 2 nd order system that consists of two successive identical 1 st order filters, so our theoretical model is applied with

B. Molecules and Precision Measurement Laboratory spectrometer

Experiments were also done with the MPML's 1.39-m dual-laser spectrometer. The apparatus has been already described in details elsewhere [10,36]. For the aims of the present study, the intensity of the probe laser was modulated by using a chopper at a frequency of about 2 kHz. Hence, phase-sensitive detection was performed by using a lock-in amplifier (Ametek, model 5209). This amplifier was also operating in the -12 dB/oct roll-off mode. From an analysis of rise times given in Ref. [START_REF]Model 5209 Single Phase Lock-In Amplifier[END_REF], it was concluded that the output filter could be considered as being a 2 nd order one with 12 Q  . Measurements were performed on the 4 41  4 40 line of the H 2 18 O  1 +  3 band at the constant temperature T of about 296 K. Line shapes were recorded at a fixed pressure P (of about 3.6 Torr, from a 97% 18 O-enriched water sample) and using various detection conditions (frequency speeds  ranging from 10 to 85 MHz/s and indicated amplifier time constants  D from 0.01 to 3 s), so that  D could be varied from 0.5 MHz up to 500 MHz (i.e. from

C. A representative example: Calibration of the detection system frequency constant

Line shapes of ammonia were recorded with the LPL's spectrometer, under identical thermodynamic conditions, with a | | = 21.8 MHz/s sweeping rate and a lock-in amplifier set to a 3 s time constant. This is 1.3 times longer than the time required for sweeping one Doppler half-width ( 49.9 MHz). Such conditions correspond to a frequency constant

MHz 130 /   Q D D     
(about 2.6 Doppler widths).  D /t was chosen to be large (equal to 44) in order to approach the continuous frequency sweeping mode. The recorded absorption signals are shown in FIG. 2. The signals were recorded in both sweep directions, once with increasing and once with decreasing frequencies (shown in the upper and lower panels, respectively). These parameters were chosen specifically to enhance deformations due to the detection system. As a result, the line shapes appear to be strongly asymmetric, exhibiting a sharp leading edge and a soft tail. They also show maximum absorption at frequencies that differ from the true centre by about 90 MHz in each direction, corresponding to a shift of the order of  D . However, it is interesting to note the mean value of these two frequencies is in agreement with the frequency obtained by saturated absorption techniques [37].

Both records have been fitted, taking the detection properties into account via an extension of Eq. ( 9) using a simple Voigt profile including the Beer-Lambert law (see section II.B and C.). In these fits, the central frequency  fit , the collisional broadening  col , the line area and the base line (level and slope) were adjusted, while fixing the Doppler broadening at its theoretical value for T273.15 K. Residuals reported in FIG. 2 show that both recorded line shapes are very well reproduced, leading to  fit frequencies that differ by 0.33 (6) This shows the importance of an accurate measurement of the lock-in time constant  D . This is especially clear from Eqs. ( 5) or (11) which show that retrieved central frequencies depend linearly on  D via  D . Thus, for calibration purposes, we must consider several measurements made at a fixed time constant  D with different ( i , t i ) sweeping conditions. Defining i fit  as the measured central frequency for an experiment i, the  D value was adjusted in order to minimize the quantity  

i i fit 2 0 ) (  
. This measures the true time constant of the lock-in detection  D , which agrees with the nominal values to within 10% or less for large  D and 20%

for the smallest ones. These values were then considered for further analysis (sections IV and V). Note that in this investigation, the Q-value remains fixed to 1/2, as Q-and  D -values are strongly correlated via the definition of the frequency constant  D .

To conclude, this experiment gives strong support to the above theoretical model and shows that an accurate characterization of the amplifier output filter is required. In particular, the time constant  D must be very well known.

IV. MOLECULAR RESONANCE FREQUENCY AND LINE SHAPE PARAMETERS RECOVERY

In this section we describe possible means of recovering the original central frequency and line shape parameters of molecular transitions. Spectra have been recorded with LPL's or MPML's spectrometers for which frequency sweeps consist of a serie of discrete steps. Depending on experimental conditions ( D /t ratio values) either the step-by-step frequency sweeping mode (section II.D) or the continuous frequency sweeping mode approximation has been used (section II.B). As no analytical line shape is presently available for the step-by-step model, line shape fitting procedure has been performed in the frame of the continuous frequency sweeping mode approximation (Eq.( 7)), whereas some consequences of the stepby-step frequency sweeping mode have been analysed using numerical simulations (numerical integration of Eq. ( 2), see section II.D).

A. Resonance frequency measurement

Several spectra of water vapor were recorded with the MPML's spectrometer in the same thermodynamic conditions, using frequency step  = 3 MHz, for increasing values of the frequency constant  D . According to section II.D, and considering chosen  D /t values (from 0.3 to 85), the frequency step influence could not be strictly neglected ( 0.25 1.0 a   ). In a first approximation, spectra have been fitted by using Eq. ( 9) in order to test resonance frequency recovery in the frame of the continuous frequency sweeping mode approximation. This was done adopting the suitable profile, a speed dependent Galatry profile, with fixed collisional broadening  col , pressure induced frequency line shift, velocity exponent m and the diffusion parameter  Gal from ref [10,36], the Doppler broadening being fixed at its theoretical value (357.05 MHz). In these fits, the central frequency  fit , the line area and the base line (level and slope) were adjusted. In FIG. 3 the retrieved line-center frequencies were plotted as a function of the frequency constant  D . If detection properties are neglected, one observes a shift of  fit proportional to  D for the lower  D values, as expected from Eqs. ( 5) or (11). For  D -values larger than about half the Doppler width, the line asymmetry becomes significant, which explains the observed non linearity. 6) THz, which is in agreement within 2×10 -8 with the expected value  0 = 215.823 684(3) THz, as provided by the HITRAN database [6]. As mentionned, considering the  D /t values, the frequency step influence is not strictly negligible. Nevertheless the continuous frequency sweeping approximation demonstrates a strong improvement on frequency measurement accuracy even for large  Dvalues. This is simply explain by the fact that the frequency shifts in the real operating mode of the spectrometer (step-by-step sweep) and the continuous frequency sweeping mode approximation remain nearly indistinguishable at the present uncertainty level (  

1. D a    is small whatever is  D ).
For the sake of completeness, numerical simulations have been performed to compare retrieved frequency in the continuous approximation and in the stepby-step numerical analysis. For the present experimental conditions, we conclude that the continuous approximation entails an underestimation of the retrieved frequency of 1.2 MHz (6×10 -9 of the expected frequency), about 2 standard deviations or less than 1/200 of the Doppler width. . Frequency steps , in the 0.5-4 MHz range, were positive or negative depending on whether laser frequency was increasing or decreasing, respectively. Although such conditions (0.4<| D | < 3.3 MHz) comply with the Ref. [START_REF] Townes | Microwave Spectroscopy[END_REF] rule, | D |/ Dop < 1/10, recorded lines are only frequency shifted, but without any significant line shape distortion. All line fits were done with the usual Voigt profile, the collisional broadening being fixed at the value expected at the sample pressure, the pressure induced line shift being neglected [START_REF] Triki | [END_REF]. Corresponding results are summarized in FIG. 4.

In a first step, line fits were done neglecting influences of lock-in time constant as well as frequency step. Retrieved frequencies  fit (plotted as ) are actually positively (resp. negatively) shifted according as the laser frequency is increasing (resp. decreasing). If the influence of the time constant  D is considered via Eq. (11), that is assuming a linear evolution of the laser frequency, shifts of retrieved frequencies (plotted as +) are inverted. This feature cannot be explained only by a calibration error in  D (a factor about 2 would be required) and suggests the influence of the step-by-step spectrometer operation. Thus, retrieved frequencies  fit have been corrected following numerical simulations (section II.D) and using Eq. ( 13). It was found that for  D = 36 ms, a value 20% larger than the 30 ms indicated one and leading to a  = 0.52, these corrected values (plotted as o) get independent of  steps. The horizontal full line displays the weighted average of these values, 28.953 694 09(8) THz, a result in agreement with the frequency obtained by saturated absorption techniques, 28.953 693 9(1) THz [37]. Moreover, it is worth mentioning that the standard deviations of the set of measurements (0.08 MHz) is comparable to individual  fit uncertainty resulting from line fits (between 0.04 and 0.11 MHz). This corresponds to a reproducibility of frequency measurements better than 10 -8 in relative value, which demonstrates the accuracy that can be actually achieved with signal-to-noise ratios about 200 when the spectrometer apparatus function is properly taken into account. The artificial frequency shifts discussed in this section are commonly canceled by recording two scans of opposite frequency sweep direction, expected to produce two spectra with opposite shifts about the true resonance value. The latter can therefore be safely recovered. However, this procedure requires a fine control of all experimental parameters during the time needed to record two spectra and a perfect control of the symmetry of the opposite frequency sweeps. The theoretical model described here enables to relax those stringent constraints. Another frequently used trick to get rid of laser frequency drifts consists in randomizing the time ordering of the discrete frequencies used to record a spectrum [41] (instead of performing a monotonous step-by-step sweep). However, note that this procedure induces a larger D  mean value, increased by about the number of discret frequencies used.

The resulting effect on the measured resonance frequency could certainly be accurately evaluated with an extension of our model, and taken into account in the uncertainty budget. Finally, we note that the detection bandwidth difficulties can be avoided by locking the laser frequency to the line center and measuring it relative to some standard, a technique allowing for very high accuracy. This approach requires a modulation of the laser frequency, with heterodyne detection (either at the first or at the third harmonic), so as to produce a dispersive signal when scanning the resonance. This profile is distorted as well, depending on the selected frequency constant. In spite of that, no effect is expected on the frequency measurement, when locking the laser to the center of the dispersive signal, as the laser scan is reduced to zero.

B. Collisional broadening measurements

The effects of the detection bandwidth on collisional broadening measurements were analyzed by performing experiments on ammonia using the LPL's spectrometer. Fixing the pressure, a series of scans in both sweep directions were recorded at different frequency constants  D ranging from 0.1 up to nearly 150 MHz. These line shapes were fitted to the Voigt model, with adjustable central frequency, collisional width, line area and base line while fixing the Doppler width at its theoretical value (an usual procedure in collisional broadening measurements). Each dataset was fitted twice: once using a normal Voigt profile, once accounting for the deformations due to the detection bandwidth via Eq. ( 7) (assuming a continuous laser frequency operation). FIG. 5 shows the measured collisional width as a function of the logarithm of | D |.

If detection properties are taken in account via Eq. ( 7) (square symbols), retrieved collisional widths are independent of the frequency constant  D , as expected. The standard deviation derived from the fits (about 0.5-1.5%) are also independent of  D . If the detection finite bandwidth is ignored (circles), for largest | D |-values the extracted collisional (i.e. Lorentz) widths  Lorentz depart strongly from the expected  col value. Such a divergence, which does not appear explicitly in lowest order terms of Eq. (11), is in fact artificially introduced when fixing the Doppler line width in the fitting procedure. From the experimental results of FIG. 5 which correspond to the Doppler regime ( col <<  Dop ), this deviation can be modeled as

2 1 3( / ) Lorentz col D Dop          .
For | D |/ Dop = 1/10, the corresponding relative broadening is about 1.5%. This means that unless we explicitly account for deformations due to the detection bandwidth, Ref. [START_REF] Townes | Microwave Spectroscopy[END_REF] condition is slightly insufficient in accounting for typical requirements in collisional broadening measurements [42]. Note that increasing and decreasing frequency experiments lead to identical results.

The line area behavior was also analyzed using the same experimental data. Within the Ref. [START_REF] Townes | Microwave Spectroscopy[END_REF] condition, | D |/ Dop < 1/10, the systematic effect induced by the detection bandwidth on line area determination remains smaller than 0.7%.

C. Line shape analysis

An accurate line shape analysis was performed on water vapor with MPML's spectrometer. FIG. 6 displays a spectrum obtained with the sweeping rate  = +32.6 MHz/s, and the indicated time constant  D = 3 s, which corresponds to the detection frequency constant  D = 196 MHz, about half the Doppler width. In such conditions, the half-width recording duration  Dop / is about 3.7 times larger than the time constant  D , to be compared to 20, the recommended minimum value [START_REF] Townes | Microwave Spectroscopy[END_REF]. By comparison with the true line center  0 , the maximum absorption is shifted by about +180 MHz, nearly half the Doppler width. However, the recorded line looks nearly undistorted at first glance.

Several line fits were performed taking account of the Beer-Lambert law. The central absorption frequency  fit , the collisional line width  col , the line area, as well as the parameters of the linear baseline were adjusted whereas  Dop remained fixed at its theoretical value. A fit to the Voigt model but neglecting actual detection properties leads to asymmetric residuals (curve b). Moreover, the retrieved collisional broadening  

5 MHz

col

  is about twice larger than the expected value [10].

The ratio  D /t has been chosen to be large enough (equal to 32) so that the continuous frequency sweeping mode approximation is valid. It has been applied by fitting line shapes using Eq. ( 9). Accounting for detection properties leads to a much better result (curve c), but still having the well known W structure in the residuals, which is characteristic of a line narrowing effect [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF]. According to [10], this departure from the Voigt profile results mainly from the dependence of collisional broadening on molecular speeds with a small contribution of the Dicke effect via velocity-changing collisions. So, a nearly perfect result (curve d) has been obtained using the symmetric version of the speed-dependent Galatry profile. In this fit, the diffusion parameter was fixed ( Gal = 0.4 MHz/Torr [10]) whereas speed dependent effects were taken into account via the hypergeometric model [10] in which the collisional broadening and corresponding velocity exponent were adjusted, leading to  

12 MHz

col   and m = 0.64 (1). These values, even being obtained from a single recording, performed with quite unusual detection properties, are reasonably good. In particular, the m-value is close to the 0.5 value given in Ref. [36].

V. DOPPLER BROADENING THERMOMETRY

One of the motivations of the present work is to further gain in the capability to make precision spectroscopic measurements devoted to metrological applications. In this section a particular emphasis is put on an accurate spectroscopic determination of the Boltzmann constant by DBT. In proof-of-principle experiments performed on NH 3 and CO 2 molecules, k B was determined with a combined uncertainty of 190 and 160 parts per million (ppm), respectively [43,44]. At the time, the spectral analysis was performed using simplified models such as gaussian and Voigt profiles. In the last few years, an ambitious goal was set to reach a target uncertainty of 1 ppm, needed for the new definition of the kelvin unit [START_REF] Bipm | Resolutions adopted by the General Conference on Weights and Measures (24th meeting)[END_REF][START_REF] Fellmuth | [END_REF][22]. The required technical improvements and upgrades of the spectrometers have been accompanied by an increasingly refined interpolation of the experimental profiles [45][46][47][48]. Particularly, a great attention is being paid to the role of speed-dependent effects [START_REF] Triki | [END_REF]49]. Also, other molecules and atoms such as Rb, H 2 18 O or C 2 H 2 are now probed [34,50,51]. Finally, there are significant efforts to produce a complete uncertainty budget, which includes the understanding and possible reduction of sources of systematical deviations [35,36].

Since the target uncertainty is in the 1 ppm range, a reliable quantification of the finite bandwidth contribution to the uncertainty budget is necessary. This is obtained through both experiments and numerical simulations based on the theoretical model of section II.

A. Doppler width measurements

In order to confirm theoretical predictions of section II, the set of measurements recorded with MPML's spectrometer and analysed in section IV.A has been once more fitted considering the continuous frequency sweeping model (a suitable approximation for this particular set of data, see section IV.A) and using the speed dependent Galatry profile. Unlike previous analyses, the Doppler width is now considered as a free parameter and collisional broadening  col , pressure-induced shift, velocity exponent m and the diffusion parameter  Gal , as fixed parameters. Note first that we draw the same broad conclusions as those outlined in section IV.A for the central absorption frequency  fit . Concerning Doppler width measurements, the results are summarised in FIG. 7 where the retrieved gaussian widths  Gauss are plotted against the logarithm of the frequency constants  D . When neglecting the The analytical model for the Butterworth 2 nd order filter with a -12 dB/oct roll-off and 1/ 2 Q  is also shown on FIG. 8 as a bold dashed line. This case is clearly more attractive because Eq. ( 12) predicts a gaussian width which is independent of  D to lowest order. As a matter of fact, for the continuous frequency sweeping case, numerical simulations show this width can be modeled as , a 4 th order polynomial dependence instead of the 2 nd order dependence of the previous cases. By contrast with the 12 Q  2 nd order filter, the continuous frequency sweeping model appears to be a lower limit: decreasing the  D /t ratios no longer reduces the observed deviations. A stronger reduction is only obtained by reducing the step size. Nonetheless, the 1 ppm target is reached with a  about 330 times smaller than  Dop but the  D /t ratio can be as large as 3.5, more than one order of magnitude larger than in the case of the 12 Q  2 nd order filter. This demonstrates the advantage of a Butterworth filter as it would allow the use of a much larger time constants  D or sweep speeds. This implies that for a fixed acquisition time, the experiment would yield better signal-to-noise ratio, so reduced experimental uncertainty, using a Butterworth filter.

It is worth noting that the recent measurement of k B at the MPML [50] was carried out under very favourable conditions, using a first order low pass filter so that  D was about 2 kHz (namely, five orders of magnitude smaller than the Doppler width), while the ratio  D /t was set to . These conditions make it possible to neglect the detection bandwidth effect in the uncertainty budget [50]. On the other hand, this contribution is larger than 10 ppm in the determination of k B reported in refs [37,47], and the ratio  D /t being set to 0.35  . This source of inaccuracy not considered at that time remains below the reported combined standard uncertainty of 50 ppm [START_REF] Mohr | [END_REF]. Nevertheless, for this project, the acquisition conditions will have to be reconsidered in order to reduce the impact of the limited detection bandwidth to below 1 ppm for future measurements.

Note that the method mentioned in section IV.A, consisting in randomising the time ordering of frequencies to get rid of frequency drifts is particularly detrimental when measuring a line-width and thus k B , as it induces a much larger D  mean value and in turn a larger impact on the recorded width, and especially the Doppler width.

VI. CONCLUSION

Precision measurements in laser spectroscopy require high signal-to-noise ratio, on the one hand, and high spectral fidelity, on the other one. A reduced detection bandwidth may have significant consequences on the observed line shape, adding asymmetries, shifting its central frequency or broadening the line. A theoretical model has been proposed for a careful analysis of these effects. In case of a continuous evolution of the laser frequency, the line shape can be set in a quasi-analytical form that allows one to consider the influence of the detection bandwidth, thus avoiding possible systematical deviations in the retrieved parameters. Numerical simulations performed in the case of a step-by-step frequency scan lead to an empirical expression for the correction to be applied to the center frequency retrieved from a fit of a distorted profile.

The model has been severely and accurately validated by applying it to the analysis of high-quality molecular spectra. The impact of the detection bandwidth could be quantified for various line shape parameters: central frequency, Doppler broadening, collisional broadening, the dependence of the latter on molecular speeds, Dicke narrowing contribution.

The dedection bandwidth induced line shape distorsion and the resulting inaccuracy in the measured parameters may impact many fields of research, from atmospheric and interstellar physics to precision spectroscopic measurements devoted to metrological applications, tests of quantum electrodynamics or other fundamental laws of nature. As an example, emphasis has been put on the repercussions on the precise determination of the Boltzmann constant by the Doppler Broadening Thermometry. Our study allows us to work out the optimum experimental conditions (integration time, frequency scan rate, type of filter, and frequency step) required to reach the targeted uncertainty of 1 ppm level of accuracy. The present study could easily be extended to other precision spectroscopic measurements in order to quantify and possibly reduce the resulting inaccuracy potentially affecting such experiments.

  A() with a slight frequency lag given approximately by the frequency constant  D .

2

 2

  the usual -12 dB/oct roll-off of a 2 nd

FIG. 1

 1 FIG. 1 shows the deviation of the centre frequency from its original value ( fit - 0 ), as a function of the frequency constant D  , for a 12 Q  2 nd order filter. Both axes have been scaled to the Doppler width. Full curves refer to various frequency steps  and dotted lines (specified by symbols) to different values of D t   . Similar behaviors were obtained for

FIG. 1 .

 1 FIG. 1. Influence of frequency sweeping conditions on the line frequency determination (2 nd order filter with Q = 1/2). Frequency deviations ( fit - 0 ) /  Dop are plotted versus frequency constant  D /  Dop for various frequency steps  /  Dop (ranging from 0.001 up to 0.1 and quoted closed to corresponding full curves).Results corresponding to some  D /t ratios are drawn in dotted lines and specified by symbols: (▲) 0.2; (•) 0.35; (■) 1.0. The thick line refers to continuous frequency sweeping model.

FILTER

  now be compared to several experiments done at the Laser Physics Laboratory (LPL) of Villettaneuse and at the Molecules and Precision Measurement Laboratory (MPML) of Caserta.

  12 Q  . Line shapes were recorded at various pressures P (ranging from 0.4 to 4.2 Torr) and using various detection conditions (frequency speeds | | ranging from 5 to 90 MHz/s and indicated amplifier time constants  D from 30 ms to 3 s), so that | D | could be varied from 0.3 MHz up to 350 MHz (i.e. from 3 6 10   up to 7 Doppler widths) and  D /t varied from 0.3 to 60.

3 1 .

 1 4 10   up to 1.4 Doppler widths) and  D /t varied from 0.3 to 85. The large signal-to-noise ratios, which were achieved in this experiment, enabled us to analyze the deviations from the Voigt profile and their influence on spectroscopic parameters (see section IV.C).

FIG. 2 .

 2 FIG. 2. Transmission of the saQ(6,3) rovibrational line of the  2 vibrational mode of14 NH 3 recorded for increasing (upper panel) and decreasing (lower panel) frequencies (see text for details). (a): recorded line; (b): unmagnified residuals from a Voigt profile fit taking the detection system properties into account ( col = 13.60(8) and 12.56(7) MHz, respectively, achieved signal-to-noise ratios  480 and 550, respectively). Frequency scale (in MHz) is shifted by 28.953 600 THz; temperature =273.15 K; pressure  1 Torr; cell length = 4.5 cm; frequency step  = 1.5 MHz; step duration t = 68.8 ms; indicated lock-in time constant  D = 3 s.

FIG. 3 .

 3 FIG. 3. Absorption frequency of the 7 199.103 cm -1 line of H 2 18 O retrieved from a speed-dependent Galatry profile. Fitted central frequencies  fit , shifted by 215.823 500 THz, are plotted against the frequency constant  D (see text for details): () uncorrected values, (o) values corrected for detection system properties; (mixed line) linear approximation; (dashed line) empirical model; (full line) weighted mean value of corrected data. Error bars (3 standard deviations) are smaller than symbols.

  To analyse in detail the influence of the frequency constant in step-by-step frequency sweeping mode, complementary experiments have been performed at LPL on ammonia, with fixed values of lock-in time constant (indicated value  D = 30 ms) and step duration (t = 74.5 ms) leading to 0

FIG. 4 .

 4 FIG. 4. Influence of the step-by-step mode on the retrieved frequency  fit . The frequency of the of the saQ(6,3) rovibrational line of the  2 vibrational mode of 14 NH 3 has been fitted using the Voigt profile (see text): () lockin time constant  D and frequency step  influences neglected; (+) continuous frequency sweeping approximation; (o) step-by-step frequency sweeping considered with  D = 36 ms; (straight line) weighted mean value of retrieved frequencies. Fitted frequency scale is shifted by 28.953 600 THz; step duration t = 74.5 ms; indicated lock-in detection time constant  D = 30 ms; temperature =273.15 K; pressure  1 Torr; cell length = 4.5 cm. For clarity, error bars are 3 standard deviations.

FIG. 5 .

 5 FIG. 5. Collisional broadening of the saQ(6,3) rovibrational line of the  2 vibrational mode of 14 NH 3 plotted against the absolute frequency constant (log plot). Sp ectra were recorded at temperature  273.15 K and pressure  1 Torr, for both increasing (open symbols) and decreasing (full symbols) frequencies; fits to a Voigt profile were performed, either by neglecting actual detection properties, circle symbols, or by correcting for them, square symbols (error bars are 3 standard deviations). Dotted line corresponds to theoretical model (see text for details). Weighted mean value from corrected data is < col > = 13.59(32) MHz.

FIG. 6 .

 6 FIG. 6. Transmission of the 7 199.103 cm -1 line of H 2 18 O recorded for increasing frequency (see text for details). (a): recorded line. Residuals (magnified by 10): (b): Voigt profile not corrected for detection system properties,  col = 93.3(5) MHz; (c): corrected Voigt profile,  col = 41.7(2) MHz; (d): corrected SD-Galatry profile,  col = 49.73(12) MHz, achieved signal-to-noise ratio  4 500. Frequency scale (in MHz) is shifted by 215.823 500 THz; Temperature = 296.073 0(4) K; pressure  3.6 Torr; cell length  30 cm; frequency step = 3 MHz; step duration = 92 ms; indicated lock-in time constant  D = 3 s.

FIG. 7 .

 7 FIG. 7. Doppler width of the 7,199.103 cm -1 line of H 2 18 O retrieved from a speed-dependent Galatry profile. Fitted gaussian widths  Gauss are plotted versus the frequency constant  D (log plot): () uncorrected values; (o) corrected values for the detection system properties (see text for details). Approximate theoretical uncorrected values: dotted line. Weighted mean value of corrected data (full line): < Gauss > = 359.1(15) MHz. Error bars are 3 standard deviations.

FIG. 8 . 1 (

 81 FIG. 8. Influence of frequency sweeping conditions on the Doppler broadening determination (2 nd order filters with Q = 1/2 and

  MHz, less than 0.2% of the 180 MHz frequency difference of maximum absorption pikes.

	It is important to note that this residual difference can be exactly canceled by setting
	the lock-in time constant to	D  	2.993 s	instead of the nominal 3s. The resulting measured
	central frequency is 28.953 694 15(5) THz, in agreement (to within 2 standard deviations)
	with the value obtained by saturated absorption techniques,	0  	  28.953 693 9 1 THz	[37].

   Dop . Their weighted mean value amounts to 215.823 688 2(

	deviation		can	be	well	modeled	using	the	empirical	expression
		fit	0    	D	2  1 0.125( / ) D Dop      . By contrast, when considering detection properties via
	Eq. (9), retrieved frequencies 
										From the retrieved values, this

fit get independent of  D , even for  D -values up to 1.3

  First consider the Q = 1/2 case. For the continuous frequency sweeping model, the We see that the target accuracy of 1 ppm will be reached if  D / Dop is smaller than the frequency step  and on the ratio  D /t. Therefore, curves corresponding to two -values have been drawn. As expected, in case of large  D /t ratios, the model is well approximated by the continuous frequency sweep. However, if this ratio gets smaller than about 0.35, the deviation from the Doppler width is strongly reduced.Although this may seem promising, this happens because the time constant  D is short, implying a reduction in the signal-to-noise ratio. Nevertheless, ignoring this last difficulty and from examination of FIG.8, we conclude that for a Q = 1/2 filter, deviations are reduced to an acceptable level for example with a frequency constant  D about 700 smaller than  Dop , frequency steps  as small as 1/330 of the Doppler width  Dop , which implies a ratio 

	relative		deviations		of			the				retrieved	Doppler	width,	given	by
		 	Gauss	  	Dop		 	Dop		0.5	 	D	 	Dop		2	as derived from Eq. (12), is drawn as a thin dotted
	line. 3 1.5 10  	. The associated numerical simulations show a more interesting result, which
	depends strongly on

D /t smaller than 0.25. Note that in the 1 st order filter case (-6dB/oct roll-off), numerical simulations lead to the same kind of requirements, if  D is chosen about 1000 smaller than  Dop .

Note that, in contrast to usual signal treatment theory, frequency and time domains are exchanged,  and  (the latter not to be confused with time t) being conjugate variables.

AKNOWLEDGMENTS

The authors acknowledge financial support from CNRS, Université Paris 13 and LNE. This work is part of projects NCPCHEM (2010 BLAN 724 3) and CaPPA (ANR-10-LABX-005 through the Programme d'Investissement d'Avenir), both funded by the Agence Nationale de la Recherche (ANR, France). François Rohart thanks Bernard Ségard for helpful discussions.

influence of detection properties, the gaussian widths, Gauss   , look weakly affected by the frequency constant up to 30 MHz, a tenth of the Doppler width. The retrieved gaussian widths can be compared to the results predicted by Eq. 12. This approximate theory, valid for small  D -values, is in agreement with observations up to  D of about 100 MHz, i.e. 1/3 the Doppler width (see the dotted curve of FIG. 7). Above this value, the extracted values deviate due to line asymmetries. By contrast, if the detection properties are taken into account in the line fitting procedure, the retrieved Doppler widths are clearly independent on  D , even for the largest values of the frequency constant. In this case, a weighted mean leads to 359.1 [START_REF] Townes | Microwave Spectroscopy[END_REF] MHz, in agreement to within 6 10 -3 with the expected Doppler width, a good result for such unusual detection conditions for time constant and/or frequency sweeping rate. Once again the continuous frequency sweeping approximation demonstrates a strong improvements of line width measurement accuracy.

Note that experiments at LPL (section IV.B) also lead to similar conclusions, namely that the retrieved gaussian width is in agreement to within less than 1% with the expected Doppler width when detection properties are considered via Eq. ( 9).

B. Application to the Boltzmann constant determination

As mentioned before, the primary motivation for this paper was to model the detection systems in DBT experiments for measuring the Boltzmann constant. So far, we have shown that the finite bandwidth of a detection system can cause distortions to the measured lineshapes, and we have introduced a model to account for these effects. Therefore, one possible approach for the spectroscopic determination of k B from here onwards would be to include this model in the spectral analysis. This would make the fitting procedure even more complicated than it is presently [35,36]. Furthermore, very precise measurements of the filter characteristics would be required, without which the final uncertainty would increase significantly. We therefore propose a simpler alternative: to operate in a region of the parameters' space where the model indicates that the effects are negligible. The purpose of this section is to determine this favorable region of the parameters' space. We note in advance that there will be competing interests: the level of signal deformation and the signal-to-noise ratio that both increase with  D . We conduct numerical simulations, similar to those outlined in section II.D for the determination of the line center except this time, we concern ourselves with the width. We generate fake distorted gaussian line shapes, which we fit using a pure gaussian function. Note that the use of a gaussian profile is valid, as collisional broadening is minimal under usual operating conditions for k B determination. We then plot the deviation of the measured width from its true value  

as a function of  D , the frequency constant. This is shown on FIG. 8 for the 2 nd order filter cases Q: 1/2 and 2 / 1 , the roll-off being -12dB/oct.

Once again, all values have been normalized to the nominal Doppler width. Note the target error tolerance, highlighted by a horizontal line at the 1 ppm level so our final k B measurements must be made in conditions where the deviation is below this line. The results of numerical simulations are shown together with the analytical result assuming a continuous frequency sweep.


Guillermo Ahumada

Juan Pablo Soto

David Carrillo

Carolina Manzur
email: cmanzur@ucv.cl

Thierry Roisnel

Jean-René Hamon
email: jean-rene.hamon@univ-rennes1.fr

Deacetylation of chiral ferrocenyl-containing β-diketones promoted by ethylene diamine: Spectroscopic and structural characterization of the fragmentation products

Keywords: Ferrocenyl, Chiral -Diketones, Ethylene Diamine, Deacetylation, Michael Addition, Retro-Mannich Rearrangement

) react with ethylene diamine under acidic conditions in refluxing toluene to yield, unexpectedly, their deacetylated counterparts, 3-ferrocenyl-butane-2-one (2a), 1-(4-methoxyphenyl)-3-ferrocenyl-butane-1-one (2b), and 1,3-bisferrocenyl-butane-2-one (2c), respectively. Such deacetylation reactions are accompagned by the formation of 2-methyl-2-imidazoline. A reaction mechanism involving an intramolecular Michael addition followed by a retro-Mannich rearrangement is suggested. The ketones 2a-c are fully characterized by analytical and spectroscopic methods. Additionally, compounds 2a and 2c are authenticated by single crystal X-ray diffraction analysis. The electrochemical behaviour of the bimetallic complex 2c is also investigated.

Introduction

Rational design and synthesis of acyclic or cyclic Schiff base metal complexes are of permanent interest [START_REF] Vigato | [END_REF][2][3][4], mainly due to their applications in numerous fields of chemistry varying from catalysis [5][6][7][8][9][10][11][12] to the synthesis of pharmaceuticals [13][14][15][16][17][18], including new functional molecular-based materials [17][18][19][20][21][22] with second-order nonlinear optical (NLO) properties [23][24][25][26][27][28][29]. In the latter case, the non-centrosymmetric crystal structure is a critical consideration for the design of materials with large secondorder nonlinearities although the chiral enantiopure compounds tend to crystallize in a non-centrosymmetrical space group [30]. In general, Schiff base ligands are easily available owing to low cost starting materials and facile synthesis. Furthermore, they show stability, high tunability and flexibility that could enable the tuning of the electronic properties and steric demands of their metal complexes [31,32]. The unsymmetrical acyclic Schiff bases are obtained by stepwise condensation of formyl-or keto-group and primary diamine precursors, whereas the mono-condensation of an appended O, N or S donor groups containing primary amine with aldehydes or ketones leads to the formation of tridentate Schiff bases, also called -half units‖ [33,34], through the imine, O, N or S donor groups and the carbonyl oxygen [35][36][37]. Their deprotonated forms, the anionic O,N,X-donor Schiff bases (X = O, N, S) can be considered as -pincer-like‖ ligands [33]. They could, therefore, serve as good chelating ligands for transition metals with, for instance, potential applications in catalysis [38,39].

Along this line, in pursuit of our research work aimed at designing new pushpull unsymmetrical Schiff base complexes exhibiting NLO properties [26], we were interested in the preparation of novel O,N,N tridentate metalloligands by reacting the three chiral ferrocenyl-containing -diketones that we reported previously [40], namely, ). Herein, we wish to describe the synthesis, the full analytical and spectroscopic characterization, and the electrochemical behaviour of the three chiral ferrocenyl-containing ketones 2a-c, as well as some mechanistic aspects of their formation. In addition, the crystal and molecu-lar structures of the monometallic complex 4-ferrocenyl-pentane-2-one (2a) and of the binuclear derivative 1,3-bisferrocenyl-butane-1-one (2c) were determined by X-ray single crystal diffraction analysis. The electrochemical behaviour of this latter complex 2c was also investigated by cyclic voltammetry.

3-(1-ferrocenylethyl)-pentane-2,4-dione (1a), 1-(4-methoxyphenyl)-2-(1- ferrocenylethyl)-butane-1,3-dione (1b),

Experimental

General experimental methods

Reactions were performed under dry dinitrogen atmosphere using standard Schlenk techniques. Solvents were dried and distilled under dinitrogen by standard methods prior to use. All chemicals were purchased from commercial sources and used

without further purification. Compounds 3-(1-ferrocenylethyl)-pentane-2,4-dione (1a), 1-(4-methoxyphenyl)-2-(1-ferrocenylethyl)-butane-1,3-dione (1b)
, and 1-ferrocenyl-2-

(1-ferrocenylethyl)-butane-1,3-dione (1c) where synthesized following our previously reported procedure [40]. Infrared spectra were recorded from KBr disks on a Perkin Elmer model 1600 FT-IR spectrophotometer, in the range 4000-450 cm -1 . 1 H and 13 PGZ 100 all in one potentiostat, using a three-electrode cell equipped with glassy carbon working, Ag/AgCl reference and platinum wire auxiliary electrodes. The ferrocene/ferricenium redox couple (FcH 0/+ ) was located at E ½ = 0.510 V, where E ½ was calculated from the average of the oxidation and reduction peak potentials.

Synthesis

General procedure

At room temperature (rt), a three necked round-bottomed flask was charged with the appropriate amount of the chiral diketone, toluene and 5 μL (0.08 mmol) of glacial acetic acid. The solution was stirred for 5 min before the addition by syringe of 1,2ethylene diamine. The reaction mixture was refluxed for 12 h, and upon cooling to rt the resulting solution was evaporated under reduced pressure to eliminate the excess of ethylene diamine and glacial acetic acid. The crude mixture was chromatographed (3 x 24 cm) using silica gel (70-230 mesh) with a mixture of hexane/ethyl acetate as eluent.

The collected solutions were dried over MgSO 4 , filtered and the solvent evaporated under vacuum.

4-Ferrocenyl-pentane-2-one (2a)

3-(1-Ferrocenylethyl)-pentane-2,4-dione: 0.50 g (1.60 mmol), toluene: 8.00 mL, 1,2 ethylene diamine: 0.10 mL (1.60 mmol), eluent: hexane/ethyl acetate (4:1).

Compound 2a was clearly observed as a yellow band (Rf: 0.9

1-(4-Methoxyphenyl)-3-ferrocenylbutane-1-one (2b)

1-(4-Methoxyphenyl)-2-(1-ferrocenylethyl)-butane-

Crystal structure determinations

X-ray data for compounds 2a and 2c were collected at 150(2) K on a Bruker APEXII AXS diffractometer, equipped with a CCD detector, using Mo-K radiation ( = 0.71073 Å). For each compound, a crystal of appropriate size was coated in Paratone-N oil and mounted on a Kaptan loop. The loop was transferred to the diffractometer, centred in the beam, and cooled by a dinitrogen flow low-temperature apparatus that had been previously calibrated by a thermocouple placed at the same position as the crystal. The structures were solved by direct methods using SIR97 [41], and then refined with full-matrix least-square methods based on F 2 (SHELXL-97) [42], with the aid of WINGX [43], with all non-hydrogen atoms being refined anisotropically. The hydrogen atoms were included in calculated positions and were refined as riding atoms with isotropic displacement parameters. A summary of the details about crystal data collection parameters and refinement are documented in Table 1. Additional crystallographic details are in the CIF files. ORTEP views are generated using OLEX2 software [44].

Results and Discussion

Syntheses and characterization

The syntheses of the organometallic ketones 2a-c were carried out in refluxing toluene, upon reacting the chiral -diketones 1a-c with an equimolar amount of ethylenediamine for 12 h, using glacial acetic acid as catalyst (see scheme 1).

Compound 2a was isolated as a yellow powder, while compounds 2b and 2c were obtained as a yellow oil and a red powder, respectively, in yields ranging between 71 and 31%, depending on the R substituent. This suggests that the steric more than electronic effect plays a significant role in the formation of the products, for which the yield decreases when the steric hindrance of the substituents of the starting diketone reagents increases. The electron donating abilities of both 4-methoxyphenyl and ferrocenyl groups are known to be similar [45]. The three organometallic ketones are air and moisture insensitive, thermally stables, and they are very soluble in solvents like dichloromethane, thf, ethyl acetate, but slightly soluble in hexane and diethyl ether.

Scheme 1 Synthesis of compounds 2a-c

Reactions were also performed in CH 2 Cl 2 as solvent, giving similar yield of 2a (70%), while 2b and 2c could not be isolated in yields higher than 10%. In addition to ketone 2a (m/z = 270), the formation of 2-methyl-2-imidazoline (m/z = 84) [46] was also observed by GC-MS as the second reaction product. Under refluxing toluene conditions, the imidazoline derivative was not detected owing to its lack of thermal stability.

The compositions and identities of 2a-c were deduced from satisfactory elemental analysis, FT-IR, multinuclear and multi-dimensional NMR spectroscopy (see Section 2.2 for details). Additionally, the crystal and molecular structures of compounds 2a and 2c were solved by X-ray diffraction analysis.

The solid-state FT-IR spectra of compounds 2a-c exhibit similar features indicating analogous molecular structures. One of the weak C-H stretching absorption bands in the 3100-3090 cm -1 range can be observed for the three compounds. On the other hand, the intense absorption bands observed in the 1714-1663 cm -1 range are due to the (C=O) stretching mode of the carbonyl group. and 2c, respectively.

X-ray crystallographic studies

Perspective views of compounds 2a and 2c with the atom labeling scheme are shown in Figs. 1 and2, while selected bond distances and angles are listed in Tables 2 and3, respectively. Ketone 2a crystallizes in the monoclinic centrosymmetric space group 4) generate a stair-type structure in compound 2a, and a chain structure in compound 2c (see Fig. 3).

Compd D-H•••A (Å) D-H (Å) H•••A (Å) D•••A (Å) D-H•••A (°) 2a C15-H16

Mechanistic aspects

The mechanism showed in Scheme 2 is similar to that described by Angelov [46], where the same specific fragmentation of an enamine was observed. In the present case, we consider two routes for the formation of the enamine: (i) the direct formation of the enamine [I], owing to the proton acidity of the tertiary central carbon of thediketone 1 (a route that has been suggested in aqueous medium catalysis [49]), and (ii) the imine [II] formation and its subsequent conversion to enamine [I]. This imineenamine tautomerism is favored by stabilization through conjugation of the carbonyl group and the carbon-carbon double bond [50][51][52][53]. In both cases, the nucleophilic attack of the amine group would be the rate-limiting step of the reaction. Subsequently, an intramolecular Michael addition reaction of the free amine onto the enamine carbon atom would form the five-membered heterocycle of intermediate [III], followed by retro-Mannich fragmentation to generate the enol derivative [IV] and the 2methylimidazole. Enols [IV] must isomerize rapidly to their respective keto tautomers 2 as none of could be identified by 1 H NMR or FT-IR spectroscopy [33]. Although

Cyclic voltammetry measurements

The electrochemical behavior of the bimetallic compound 2c was investigated by cyclic voltammetry in dichloromethane solution containing 0.1 M n-Bu 4 N + PF 6 -as supporting electrolyte. The measurements were carried out using 1.0 mM solution of 2c

at room temperature in the potential range of +1.5 to -1.0 V, with scan rate of 100 mV s - 1 . Cyclic voltammogram (CV) of the solution containing 2c shows one chemically reversible oxidation process with current ratio i pa /i pc equal to unity, at E 1/2 value identical, within the experimental errors, to that of the FcH 0 /FcH + couple (E 1/2 = 0.510 V) taken as internal reference. The anodic to cathodic peak-to-peak separations is similar to that observed for free ferrocene under identical conditions, indicating that it is likely a one-electron oxidation of the 1-ferrocenylethyl entity to its ferricenium counterpart 2c + at the electrode. In addition, the CV of 2c exhibited also a second reversible wave at E 1/2 = 0.760 V, attributable to the mono-electronic oxidation of the ferrocenoyl moiety. Such a strong positive shift (0.250 V) with respect to free ferrocene, is presumably due to the electron withdrawing effect of the cationic [Fc-CH(CH 3 )-CH 2 -C(=O)] + substituent. This value is identical to that found for acetylferrocene [54],

suggesting that there is no electronic interaction between the two ferrocenyl moieties separated by four single bonds

Conclusions

In the present work we describe the reactivity of chiral ferrocenyl-containingdiketones toward ethylene diamine and the full analytical and spectroscopic characterization of the resulting monoketonic products. In addition, the mononuclear complex 2a and the bimetallic derivative 2c were authenticated by means of X-ray diffraction analysis. The three starting chiral -diketones follow a similar fragmentation pathway according to a domino sequence of intramolecular Michael addition and retro-Mannich rearrangement, giving rise to their respective deacetylated counterparts and formation of 2-methyl-2-imidazoline, a class of compounds that have attracted considerable attention in recent years in the development of compounds with pharmacological properties [55].

  and 1-ferrocenyl-2-(1-ferrocenylethyl)-butane-1,3-dione (1c), with 1,2-ethylenediamine through a Schiff base monocondensation reaction. Unexpectedly, we isolated the fragmentation products Fc-CH(CH 3 )CH 2 C(=O)R (R = Me, 2a; 4-MeO-C 6 H 4 , 2b; Fc, 2c; Fc = ( 5 -C 5 H 5 )Fe( 5 -C 5 H 4 )

The 1 H

 1 NMR spectra of complexes 2a-c recorded at 298 K in CDCl 3 , are consistent with the proposed structures. In each1 H NMR spectrum, the [FcCH(CH 3 )CH 2 -] fragment is clearly identified by the following characteristic multiplicity scheme; the ferrocenyl fragment consists in a group of three signals in the range 3.96-4.41 ppm which are assigned to the free C 5 H 5 ring, and to the two types of protons (H  and H ) of the substituted cyclopentadienyl ring with the integration ratio 5:2:2. This contrasts with the spectra of their respective precursors 1a-c where the two pairs of diastereotopic H  ,H ' and H ,H ' protons give rise to four resonances integrating each for 1 H[40]. The singlets observed in the 1.13-1.56 ppm range were attributed to the methyl protons while the resonances appearing in the 2.97-3.08 ppm and 2.50-2.98 ppm ranges were attributed to the proton resonances of the -CH-and -CH 2 -units, respectively. Again, the two diastereotopic protons of the CH unit are not distinguished. In addition, the sharp peaks at 2.02 ppm for 2a, 3.87 ppm for 2b and 4.10 ppm for 2c, are unambiguously assigned to the methyl, the methoxy and the free cyclopentadienyl protons of the carbonyl substituent, respectively.The13 C NMR spectra of complexes 2a-c confirm the behavior observed in 1 H NMR spectra. For the [Fc-CH(CH 3 )-CH 2 -] fragment, the ferrocenyl moiety resonates as four signals with classical chemical shifts, instead of the six resonances expected for the two pairs of diastereotopic C  and C carbons [40]. The signals observed in the 19.82-20.77 ppm, 28.01-29.40 ppm and 48.02-55.48 ppm ranges were attributed to the CH 3 , CH and CH 2 carbon atoms, respectively. On the other hand, the carbonyl carbons showed up in the expected low-field region at 208.0, 197.96 and 202.18 ppm for 2a, 2b

P2 1 /Fig. 1 Table 2 Fig. 2 Table 3

 11223 Fig. 1 Molecular structure of 2a with the atom numbering schemes. Hydrogen atoms have been omitted for clarity. Thermal ellipsoids are drawn at 50% probability.

Fig. 3

 3 Fig. 3 Intermolecular hydrogen bond interactions forming a stair-type structure in 2a (left), and a chain structure in 2c (right)

Scheme 2

 2 Scheme 2 Proposed mechanism for the formation of ketones 2a-c

  CH 3 -O), 4.42 (br s, 9 H, C 5 H 4 and C 5 H 5 ), 6.93 (d,3 J HH = 7.1 Hz, 2 H, C 6 H 4 ),7.92 (d,3 J HH = 7.1 Hz, 2 H, C 6 H 4 ).13 C { 1 H} NMR (100 MHz, CDCl 3 ): 20.77 (CH-CH 3 ), 29.40 (CH-CH 3 ), 47.16 (OCH 3 ), 55.48 (CH 2 ), 65.90 (C  C 5 H 4 ), 68.05 (C C 5 H 4 ), 69.43 (C 5 H 5 ), 90.63 (C ipso C 5 H 4 ), 113.70 (C ipso C 6 H 4 ) 130.43 (C 6 H 4 ) 130.48 (C 6 H 4 ) 163.37 (C ipso C 6 H 4 OMe), 197.96 (C=O).

	2.2.4. 1,3-BisFerrocenyl-butane-2-one (2c)
	1-Ferrocenyl-2-(1-ferrocenylethyl)-butane-1,3-dione: 0.20 g (0.45 mmol),
	toluene: 5.0 mL, 1,2-ethylene diamine: γ0 μL (0.45 mmol), eluent: hexane/ethyl acetate
	(3:2). Compound 2c was clearly observed as an orange band (Rf: 0.5). Yield: 0.06 g

1,3-dione: 0.31 g (0.77 mmol), toluene: 5.0 mL, 1,2-ethylene diamine: 50 μL (0.77 mmol), eluent: hexane/ethyl acetate (4:1). Compound 2b was clearly observed as a yellow band (Rf: 0.8). Yield: 0.140 g (0.390 mmol, 50%) of a yellow oil. Anal. Calcd for C 21 H 22 FeO 2 (362.25 g mol - 1 ): C, 69.62; H, 6.12. Found: C, 69.52; H, 6.09. IR (KBr, cm -1 ): 3094(w) ν(C-H arom), 2962(w), 2921(w), 2850(w) ν(C-H, aliph), 1675(vs) ν(C=O). 1 H NMR (400 MHz, CDCl 3 ): 1.13 (br s, 3 H, CH 3 -CH), 2.98 (br s, 2 H, CH 2 ), 3.09 (br s, 1 H, CH-CH 3 ), 3.87 (s, 3 H, (0.13 mmol, 31%) of a red solid. Suitable single crystals for the X-ray studies were obtained by slow diffusion of n-hexane into a dichloromethane solution at rt. M.p: 148-149 °C. Anal. Calcd for C 24 H 24 Fe 2 O (440.14 g mol -1 ): C, 65.49; H, 5.50. Found: C, 65.66; H, 5.79. IR (KBr, cm -1 ): 3089(w) ν(C-H arom), 2962(w), 2928(w) 2861(w) ν(C-H, aliph), 1663(vs) ν(C=O). 1 H NMR (400 MHz, CDCl 3 ): 1.14 (br s, 3 H, CH-CH 3 ), 2.82 (br s, 2 H, CH 2 ), 2.97 (br s, 1 H, CH-CH 3 ), 4.10 (s, 5 H, C 5 H 5 FcCO), 4.31 (br s, 9 H, C 5 H 4 and C 5 H 5 ), 4.41 (br s, 2 H, C 5 H 4 /FcCO), 4.69 (br s, 2 H, C 5 H 4 /FcCO). 13 C { 1 H} NMR (100 MHz, CDCl 3 ): 19.82 (CH-CH 3 ), 28.01 (CH-CH 3 ), 48.03 (CH 2 ), 66.52 (C  C 5 H 4 ), 67.93 (C C 5 H 4 ), 68.42 (C 5 H 5 ), 78.49 (C ipso C 5 H 4 ), 68.78 (C  C 5 H 4 ), 69.62 (C C 5 H 4 ), 71.16 (C 5 H 5 ), 96.61 (C ipso C 5 H 4 ) 202.18 (C=O).

Table 1

 1 Crystallographic data and details of data collection and structure refinement

	parameters for compounds 2a and 2c
		2a	2c
	Empirical formula Formula mass (g mol -1 )	C 15 H 18 Fe O 270.15	C 48 H 48 Fe 4 O 2 880.26
	Collection T (K)	150 (2)	150 (2)
	Crystal system	Monoclinic	Triclinic
	Space group	P2 1 /a	P-1
	a (Å)	8.7077(6)	11.4691(10)
	b (Å)	9.8497(8)	12.9925(9)
	c (Å) α (°)	15.3006(12) 90	14.1008(13) 66.749(3)
	ß (°) (°) V (Å 3 )	104.733(3) 90 1269.16(17)	81.895(3) 81.289(3) 1900.6(3)
	Z	4	2
	Dcalcd (g cm -3 )	1.414	1538
	Crystal size (mm)	0.6 x 0.5 x 0.14	0.31 x 0.11 x 0.03
	F(000)	568	912
	Absorption coefficient (mm -1 ) θ range (°)	1.168 3.18 to 27.45	1537 1.58 to 27.47
	Range h,k, l	-10/11, -12/12, -19/19	-14/14, -16/16, -18/18
	No. independent refl.	20473	18975
	No. unique refl. (>2)	2861	8492
	Comp. to  max (%)	99.0	99.5
	Max/min transmission	0.849/0.662	0.955/0.764
	Data/restraints/parameters	2861/0/156	8492/0/489
	Final R indices [I>2(I)]	R1 a = 0.0878, wR2 b = 0.2577	R1a = 0.0522, wR2b = 0.1344
	R indices (all data)	R1 a = 0.0933, wR2 b = 0.2607	R1 a = 0.1254, wR2 b = 0.183
	Goodness of fit/F 2	1.108	0.994
	Largest diff. peak/hole (e A -3 )	3.709/-2.007	0.616/-0.73

Table 4

 4 Hydrogen bond interactions parameters for compounds 2a and 2c

Acknowledgements

The authors thank Dr. S. Sinbandhit (CRMPO, Rennes) for helpful assistance with NMR experiments. This research has been performed as part of the Chilean-French International Associated Laboratory for ‗'Inorganic Functional Materials'' (LIAMIF-

CNRS N°836)

Financial support from the Fondo Nacional de Desarrollo Científico y Tecnológico [FONDECYT (Chile), grant no. 1090310 (C.M. and D.C.)], the Vicerrectoría de Investigación y Estudios Avanzados, Pontificia Universidad Católica de Valparaíso, Chile (C.M. and D.C.), the CNRS and the Université de Rennes 1 is gratefully acknowledged. G.A. Thanks the CONICYT (Chile) for support of a graduate student fellowship.

Appendix A. Supplementary material CCDC 1007151 (for 2a) and 1007152 (for 2c) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.as.uk/data_request/cif.


Lionel Médini

Michaël Mrissa

Jean-Paul Jamont

Nicolas Le Sommer

Jérôme Laplace

Leveraging cyber-physical objects through the concept of avatar

Context

Connected objects, assistance robots and co-workers (co-Bots) will be a major market in a near future. The Web of Things (WoT) will lead to the development of advanced applications connecting heterogeneous objects. This is an opportunity for hardware and software vendors to occupy a strategic position on new marketplaces such as those envisioned by the Compose project 1 . Such applications shall attract customers with smart interaction possibilities and seamless deployment on various ranges of devices.

The ASAWoO (Adaptive Supervision of Avatar/Object Links for the Web of Objects) project aims at building an architecture to provide users with understandable functionalities exposed as WoT applications. This architecture is designed to fully integrate physical appliances into the Web and to enable collaboration between heterogeneous objects, from the basic sensor to the complex robot.

Vision

Our vision for achieving this goal is to associate each physical object with a computer object called an avatar. Avatars are designed to:

-Expose objects as resources on the Web: avatars can be invoked using semanticenabled service-oriented protocols -Compose collaborative functionalities: they interact with the avatars of other objects to negotiate and fulfill requests requiring complex functionalities, thus enabling inter-object collaboration.

-

Manage context adaptation: they can adapt objects behavior according to their surrounding environmental changes.

-

Cope with pervasive setups: they allow network communication disruptions and support optimized communications with remote objects -Deploy code on the objects: they either deploy application code modules onto the objects or execute them in a cloud infrastructure if objects do not have enough resources to do so.

The objective of this project is to design and develop such avatars, as well as the WoT infrastructure they evolve in, together with the languages and protocols that will facilitate the integration of connected objects into the Web.

Scientific challenges

The ASAWoO project addresses several scientific locks in the following domains:

3.1. Semantic Web Several works have been / are currently conducted in the field of the Semantic Web of Things (SWoT). The best known are the Semantic Sensor Networks ontology, as well as other vocabularies that describe the different parts of connected objects (actuators, network interfaces, processing capabilities). Nevertheless, in order to use semantic tools to achieve various avatar processing tasks (e.g. functionality discovery and exposition in REST, protocol adaptation or code deployment…), several other vocabularies must be combined for the different descriptions implied by our avatar architecture.

To be able to use these descriptions even when they are disconnected, object must embed avatars with minimal reasoning capabilities, compatible with their limited resources. Such reasoners must be designed almost on purpose wrt. the processing needs and the complexity of the ontology construct must be studied and reduced accordingly.

Web services

In order to benefit from explicit data semantics in the service protocol stack, Semantic Web Services (SWS) rely on semantic Web technologies to annotate service descriptions. Semantic service-oriented architectures have not been designed to describe the capabilities of physical objects. Moreover, HTTP with its request-response paradigm is not always suitable for controlling the behavior of complex objects over the Web. Recent M2M protocols such as COAP or MQTT have been designed but still lack semantics. A major scientific challenge consists in embedding semantics in low-energy applicative protocols, to enable semantic processing inside constrained objects.

Another challenge resides in handling the complexity of the physical world in the semantic service composition task. Indeed, service composition in ubiquitous environments differs from typical composition due to the fast evolution of environmental conditions, which require dynamic techniques for adapting service composition on-the-fly according to context evolution, to provide end users with an optimal solution. In such cases, we talk about adaptive service composition [START_REF] Quan | Configurable Composition and Adaptive Provisioning of Web Services[END_REF].

Multi-Agent Systems

Models developed in MAS are inspired from human, social and cognitive sciences. They are mainly organizational models (self-organization process, hierarchy management…), interaction/negotiation models (contract net protocol, recruiting interaction protocol…), physical environment models and user models (implementation of user's behaviors fulfilling specific needs). These facets of the whole system are integrated in the agent architectures. The first challenge consists in rethinking state-of-the-art agent architectures and multi-agents models according to (semantic) Web standards.

Secondly, an avatar evolves in an environment that it can perceive and in which it acts. It is endowed with autonomous behaviors and has its own objectives. An avatar society consists in a set of avatars situated in a common environment, which interact and attempt to reach a set of goals. Through these interactions, global, intelligent and unpredictable behaviors can emerge. Our goal will be to expose such emerging behaviors as new WoT applications and study their accuracy in regard of the users' needs.

Disruption-Tolerant Networking

Due to the mobility of the robots or of the end users, and of the limitation of the communication range of the wireless interfaces, some connectivity disruptions can appear, and connectivity islands can be formed. In such conditions, it is impossible, to maintain end-to-end paths between different islands thanks to Internet legacy protocols.

In order to address these issues, we plan to define and to implement in the ASAWoO project a specific routing protocol relying on disruption tolerant networking [START_REF] Zhang | Routing in Intermittently Connected Mobile Ad Hoc Networks and Delay Tolerant Networks : Overview and Challenges[END_REF] (or opportunistic networking [START_REF] Conti | Multihop Ad Hoc Networking : The Reality[END_REF]) techniques. These techniques implements the "store, carry and forward" principle, whose basic idea is to take advantage of radio contacts between devices to exchange messages, while exploiting the mobility of these devices to carry messages between different parts of the network. Two devices can thus communicate even if there never exists any end-to-end path between them.

Contextual adaptation

Modeling contextual data at the semantic level [4] allows aggregating heterogeneous data into a "contextual situation" and therefore deriving complex adaptation processes [5]. We aim at embedding, inside each object avatar, a context management component that: 1) aggregates data from the appliance sensors (camera, GPS…) and from external services into such contextual situations; 2) will both be able to query such data and accept events that generate them due to environmental changes; 3) will be queried by other avatar component to make adaptation decisions at different levels: exposition of the object functionalities, collaboration with avatars of other objects, communication protocol between the avatar and the object, location (on the object processor or in the cloud) to deploy each WoT application module.

Technical aspects

The design, implementation and deployment of the avatar architecture led us to face several technical problems and make the following choices.

In our WoT infrastructure, objects are connected to a common gateway, located in a supposedly secured local network (e.g. smart home, enterprise supply chain). Such a gateway provides multiple connectivity interfaces (Ethernet, USB, Wifi, Zigbee…) and relies on the AllJoyn™2 interoperability framework. It is related to a dedicated cloud infrastructure that provides additional processing capabilities and a collaboration space to the object avatars.

The avatar architecture is a distributed service-oriented architecture (SOA), partly located in the cloud infrastructure and partly on the object. It is implemented in Java as a set of OSGi services that can be dynamically deployed on one of these two sides. So can be the modules of the WoT application currently executed by the avatar-object couple. To do so on objects that cannot run Java VMs, the framework and services have to be crosscompiled to fulfill our infrastructure requirements. Learn more about this project at http://liris.cnrs.fr/asawoo/.

Acknowledgements

Conclusion

The ASAWoO project concretizes existing work from the Web service and semantic Web research fields, leads to context-aware solutions for dynamic code deployment on constrained devices and disruption-tolerant routing protocols and allows defining new agent interaction models for physical objects. Its key concept is the notion of avatar.

While writing this paper, the project has already started. The avatar architecture has been defined and is currently being implemented. Semantic aspects of the functionality discovery process are presented in [START_REF] Mrissa | Semantic Discovery and Invocation of Functionalities for the Web of Things[END_REF] and collaborative advances in [START_REF] Jamont | A Web-based agent-oriented approach to address heterogeneity in cooperative embedded systems[END_REF]. Networking solutions and deployment of the WoT application modules are also under development.

We envision several benefits from the ASAWoO project. Our WoT infrastructure will provide a scalable, out-of-the-box framework enabling high-level interaction with sets of heterogeneous objects via the deployment of Web of Things applications. Object-avatars couples define cyber-physical objects that augment the built-in functionalities of physical objects.

  ASAWoO is a 4-year research project (2014-2017), funded by the French National Agency for Research (ANR), in the context of the INFRA program, under the reference <ANR-13-INFR-012>.

http://www.compose-project.eu/

https://www.alljoyn.org/