Clément Livache

Nicolas Goubet

Bertille Martinez

Amardeep Jagtap

Junling Qu

Sandrine Ithurria

Mathieu G Silly

Benoit Dubertret

Emmanuel Lhuillier

Band Edge Dynamics and Multiexciton Generation in Narrow Band Gap HgTe Nanocrystals

Keywords: HgTe, narrow band gap nanocrystals, mid infrared, band edge dynamics, multi-exciton generation, photodetection

Mercury chalcogenide nanocrystals and especially HgTe appear as an interesting platform for the design of low cost mid infrared (mid-IR) detectors. Nevertheless, their electronic structure and transport properties remain poorly understood and some critical aspects such as the carrier relaxation dynamics at the band edge have been pushed under the rug. Some of the previous reports on dynamics are setup limited and all of them have been obtained using photon energy far above the band edge. These observations raise two main questions: (i) what are the carrier dynamics at the band edge and (ii) should we expect some additional effect (multiexciton generation or MEG) as such narrow band gap materials are excited far above the band edge? To answer these questions, we developed a high bandwidth setup which allows us to understand and compare the carrier dynamics resonantly pumped at the band edge in the mid-IR and far above the band edge. We demonstrate that fast (>50 MHz) photoresponse can be obtained even in the mid-IR and that MEG is occurring in HgTe nanocrystal arrays with a threshold around three times the band edge energy. Furthermore the photoresponse can be effectively tuned in magnitude and sign using a phototransistor configuration.

INTRODUCTION

Nanocrystals are promising building blocks for the design of low cost and high performance optoelectronic devices, [START_REF] Talapin | Prospects of Colloidal Nanocrystals for Electronic and Optoelectronic Applications[END_REF] spanning from light emitting diodes, 2 lasers, [START_REF] Fan | Continuous-Wave Lasing in Colloidal Quantum Dot Solids Enabled by Facet-Selective Epitaxy[END_REF][START_REF] Geiregat | Continuous-Wave Infrared Optical Gain and Amplified Spontaneous Emission at Ultralow Threshold by Colloidal HgTe Quantum Dots[END_REF][START_REF] Lim | Optical Gain in Colloidal Quantum Dots Achieved with Direct-Current Electrical Pumping[END_REF] solar cells [START_REF] Mcdonald | Solution-Processed PbS Quantum Dot Infrared Photodetectors and Photovoltaics[END_REF][START_REF] Konstantatos | Collidal Quantum Dot Optoelectronics and Photovoltaics[END_REF] and more recently infrared (IR) photodetectors. [START_REF] Lhuillier | Recent Progresses in Mid Infrared Nanocrystal Optoelectronics[END_REF][START_REF] Kershaw | Narrow Bandgap Colloidal Metal Chalcogenide Quantum Dots: Synthetic Methods, Heterostructures, Assemblies, Electronic and Infrared Optical Properties[END_REF] The field of IR photodetection remains led by epitaxially-grown semiconductors made of II-VI (HgCdTe) and III-V (InSb, InGaAs) materials and their heterostructures (GaAs/AlGaAs). However, the cost of such technologies remains prohibitive and limits the use of IR camera to niche markets such as defense and astronomy. Expansion of IR camera to a mass market scale requires a severe cost disruption which is unlikely to result from historical technologies. [START_REF] Rogalski | Infrared Detectors[END_REF] Nanocrystals appear as an interesting alternative which may bridge the gap between expensive high cost, high performances photon detectors and the low cost, lower performances thermal detectors.

Among potential candidates to address the mid-infrared range of wavelengths, mercury chalcogenides (HgX) are by far the most advanced material to tackle this challenge. [START_REF] Kovalenko | Colloidal HgTe Nanocrystals with Widely Tunable Narrow Band Gap Energies: From Telecommunications to Molecular Vibrations[END_REF][START_REF] Chen | Mercury Telluride Quantum Dot Based Phototransistor Enabling High-Sensitivity Room-Temperature Photodetection at 2000 Nm[END_REF][START_REF] Abdelazim | Room Temperature Synthesis of HgTe Quantum Dots in an Aprotic Solvent Realizing High Photoluminescence Quantum Yields in the Infrared[END_REF][START_REF] Keuleyan | Mid-Infrared HgTe Colloidal Quantum Dot Photodetectors[END_REF] HgX colloidal quantum dots (CQDs) combine a tunable absorption from the visible range up to the THz range [START_REF] Lhuillier | Infrared Photodetection Based on Colloidal Quantum-Dot Films with High Mobility and Optical Absorption up to THz[END_REF] with photoconductive properties. [START_REF] Lhuillier | Mid-Infrared HgTe/As2S3 Field Effect Transistors and Photodetectors[END_REF] While intraband transition (as in HgSe or HgS) appears as an emerging path for the design of CQDs based IR photodetector, [START_REF] Lhuillier | Infrared Photodetection Based on Colloidal Quantum-Dot Films with High Mobility and Optical Absorption up to THz[END_REF][START_REF] Deng | Colloidal Quantum Dots Intraband Photodetectors[END_REF] their overall level of performance remains weaker that the one of interband systems based on HgTe. [START_REF] Lhuillier | Recent Progresses in Mid Infrared Nanocrystal Optoelectronics[END_REF] Moreover, HgTe CQDs benefit from their proximity with the HgCdTe alloy in terms of electronic structure knowledge and material processing. In spite of recent impressive progresses such as the development of multispectral detectors, [START_REF] Lhuillier | Electrolyte-Gated Colloidal Nanoplatelets-Based Phototransistor and Its Use for Bicolor Detection[END_REF][START_REF] Tang | Scalable Fabrication of Infrared Detectors with Multispectral Photoresponse Based on Patterned Colloidal Quantum Dot Films[END_REF] the report of first photovoltaic device based on HgTe CQDs [START_REF] Guyot-Sionnest | Background Limited Mid-Infrared Photodetection with Photovoltaic HgTe Colloidal Quantum Dots[END_REF] , the coupling to plasmonic structures to enhance the photoresponse [START_REF] Chen | Photocurrent Enhancement of HgTe Quantum Dot Photodiodes by Plasmonic Gold Nanorod Structures[END_REF][START_REF] Yifat | Mid-IR Colloidal Quantum Dot Detectors Enhanced by Optical Nano-Antennas[END_REF] or tune the spectral response [START_REF] Tang | Plasmon Resonance Enhanced Colloidal HgSe Quantum Dot Filterless Narrowband Photodetectors for Mid-Wave Infrared[END_REF] , some central questions are still unaddressed. Among them, the question of the carrier dynamics at the (narrow) band edge remains open. From an applied perspective, this question is of utmost interest since it relates to the detection bandwidth. Overall, detectors based on HgTe CQDs have been reported to be fast detectors with a µs to ms time response. [START_REF] Lhuillier | Thermal Properties of Mid-Infrared Colloidal Quantum Dot Detectors[END_REF][START_REF] Liu | N-and p-Type HgTe Quantum Dot Films[END_REF] Nevertheless, in most of the reports the probed dynamics are setup-limited or, even worse, dynamics are probed using photon energies far above the band edge, typically using pulsed lasers and diodes in the visible [START_REF] Chen | Photocurrent Enhancement of HgTe Quantum Dot Photodiodes by Plasmonic Gold Nanorod Structures[END_REF] and near IR. [START_REF] Guyot-Sionnest | Background Limited Mid-Infrared Photodetection with Photovoltaic HgTe Colloidal Quantum Dots[END_REF] These observations raise two main questions: (i) what are the carrier dynamics at the band edge in narrow band gap nanocrystals or, in engineer words, how fast is the mid-IR bandwidth? and (ii) should we expect some additional effect (multiexciton generation (MEG), hot electrons…) as such narrow band gap CQDs are excited far above the band edge?

Investigating the dynamics in mid-IR nanocrystals is especially challenging. Time resolved spectroscopic methods such as time resolved photoluminescence (PL), transient absorption and ultrafast pump-probe experiments are widely used in the visible range to probe a wide range of effects in nanocrystals such as hot exciton relaxation or MEG [START_REF] Kambhampati | Hot Exciton Relaxation Dynamics in Semiconductor Quantum Dots: Radiationless Transitions on the Nanoscale[END_REF][START_REF] Kambhampati | Unraveling the Structure and Dynamics of Excitons in Semiconductor Quantum Dots[END_REF] . However, their use in the mid IR faces two main difficulties which are the intrinsically low PL efficiency of IR emitters and the lower efficiency of IR setup (less efficient power sources and detectors). As a result, new approaches have to be developed. Recently Livache et al reported time resolved photoemission as a possible alternative path to probe carrier dynamics in near IR HgTe nanoplatelets. [START_REF] Livache | Charge Dynamics and Optolectronic Properties in HgTe Colloidal Quantum Wells[END_REF] In this article we have used a nanosecond (ns) pulsed, high power density quantum cascade laser (QCL) to probe the carriers dynamics almost resonantly with the band edge. We demonstrate that band edge relaxation is faster than 10 ns, which is promising for the design of very high bandwidth setup based on colloidal nanocrystal including in the mid IR range.

Moreover, with their extremely small band gap (270meV), HgTe CQDs are an interesting platform for the investigation of MEG/hot electron effects in nanocrystals. We consequently expand the investigation of the carrier dynamics while the CQDs are excited far (up to six time) above the band edge energy. We reveal that (i) MEG occurs in such QD at a threshold which is around 3 times the band edge and (ii) thanks to a large bandwidth setup, phototransport occurs via multiple trapping transport which can be used to estimate the sub band gap density of state.

Finally, in the last part of the paper, we demonstrate that the photoresponse of such CQDs can be fully controlled by the addition of a gate. Device performances can be improved thanks to the control of carrier density: photoresponse increases under holes injection and decreases under electrons injection, up to the point that the sign of the photoresponse can even be tuned.

METHODS

Chemicals

Mercury chloride (HgCl2, Strem Chemicals, 99%), tellurium powder (Te, Sigma-Aldrich, 99.99%), trioctylphosphine (TOP, Cytek, 90%), oleylamine (Acros, 80-90%), dodecanethiol (DDT, Sigma-Aldrich, 98%), 1,2,ethanedithiol (EDT, Fluka, 98.0%), hydrochloric acid (HCl, Mieuxa, 25%), lithium perchlorate (LiClO4, Sigma-Aldrich, 98%), polyethylene glycol (PEG, Mw = 6kg.mol -1 ), chloroform (Carlo Erba), ethanol absolute anhydrous (Carlo Erba, 99.9%), methanol (Carlo Erba, 99.8%), acetone (Carlo Erba, 99.8%), n-hexane (Carlo Erba), n-octane (SDS, 99%), toluene (Carlo Erba, 99.3%),. All chemical are used as received, except oleylamine which is centrifuged before used. Mercury compounds are highly toxic. Handle them with special care.

HgTe QDs synthesis

HgTe quantum dots with band edge cutoff around 2000 cm -1 are synthesized with a modified protocol from the reference. [START_REF] Keuleyan | Mercury Telluride Colloidal Quantum Dots: Electronic Structure, Size-Dependent Spectra, and Photocurrent Detection up to 12 Μm[END_REF] 27 mg of HgCl2 and 10 mL of oleylamine are degassed under vacuum at 120°C in a 50 mL three-neck flask. A pre-heated solution made of 100 µL of TOP:Te and 9.9 mL of oleylamine is injected into the flask. One has to note that pre-heating is essential to synthesize nanocrystals with low size dispersion. The solution color quickly changes from light yellow to dark-brown. After 3 min, the reaction is quenched with an injection of a solution of 1 mL of dodecanethiol and 9 mL of toluene. The temperature quickly drops to 70-80°C. Resulting solution is precipitated with addition of 90 mL ethanol and then centrifuged. The precipitate is redispersed in chloroform and four drops of dodecanethiol are added. A second washing step is carried out with 80 mL of methanol. The stability of the final colloidal solution is improved by redispersing the nanocrystals in chloroform.

Au/Glass electrodes fabrication

Microscope glass slides cut in half are cleaned by sonication in acetone and rinsed with isopropanol, then receive a 5 min oxygen plasma cleaning. An adhesion primer (TI-PRIME) is spin-coated onto each substrate before AZ5214E resist is spin-coated and baked at 110°C for 90s. A MJB4 mask aligner is used to expose the substrates to UV light for 2 s through a lithography mask. Black paper is put under the glass slides to prevent light from being reflected back to the resist. Substrates are then baked at 125°C for 2 min to invert the resist and flood-exposed for 15 s with the mask aligner, again using black paper. Resist is developed using AZ326 developer for 20 s and rinsed with pure water. Patterned substrates are dried and cleaned with 5 min of oxygen plasma to remove resist residues. In a thermal evaporator, 5 nm of chromium are deposited as an adhesion promoter before 80 nm of gold are evaporated. Lift-off is conducted in an acetone bath for at least one hour. Electrodes are 2.5 mm long and spaced by 20 µm.

PET/ITO electrodes

A PET/ITO wafer is cleaned using acetone and isopropanol. AZ5214E resist is spin-coated and baked at 110°C for 90s. Substrates are exposed to UV light for 4 s through a mask, then dipped into a AZ326 developer bath. Electrodes are then etched using 25% HCl for 10 s and rinsed with pure water. Electrodes are 1 mm long and spaced by 20 µm.

Electrolyte preparation

In our top-gated FET geometry, we use a quasi-solid electrolyte prepared as follows. In a glove box, 0.5 g of LiClO4 are mixed with 2.3 g of PEG (MW = 6 kg.mol -1 ). The resulting mix is heated at 170°C for 2 h until the solution turns transparent.

Device preparation

In a nitrogen-filled glove-box, pre-patterned interdigitated gold electrodes (20 digits, 20 µm separation) on glass substrate are dipped in a solution of HgTe QDs in chloroform. The substrate is tilted to allow the excess solution to drip, ensuring a smooth and homogenous coating. Ligand exchange is performed by dipping the film in a ethanedithiol (EDT) solution in ethanol (1% w/) for 90 seconds and rinsing it in pure ethanol for 30 seconds. This process is repeated 3 times to fill the cracks and reach a device resistance of 10 to 40 kΩ.

FET device preparation and measurements

First, a regular device is prepared in air-free conditions using the protocol described above. An electrolyte (PEG 6k + LiClO4) is heated at 90°C and brushed atop of the device and allowed to solidify in the glove-box for two hours. Drain, source and gate electrodes are then connected to the outputs of a Keithley 2634b dual-channel source-meter controlled by a LabView software. Transfer curves are acquired by setting the drain voltage to 100 mV and sweeping the gate voltage at a 10 mV/s rate. Both drain and gate currents are monitored and the full cycle is repeated 2 times to ensure stable operation.

I-T curves under dark condition

The sample is connected in an closed-cycle cryostat and biased under 1 V by a Keithley 2634 source-meter. The sample is cooled down from 300 K to 15 K while current and temperature are measured every 200 ms.

Temperature-resolved CW measurements

The sample is connected in a cryostat and biased (1 V) using a Keithley 2634b source-meter. Illumination is provided through a glass window by 4.4 µm QCL. The transparency of the glass window for MIR pulses is around 30% and is accounted for in the presented data. Data are acquired using the Keithley 2634b source-meter through a homemade LabView program.

GHz time-resolved photocurrent measurements in the MIR

The sample is connected in a cryostat (for temperature-resolved measurements) or in an open sample holder, and biased using a 9 V battery. Illumination is provided by 20 to 500 ns pulses from a 4.4 µm QCL laser (MirSense) operated at 200 kHz. Transient photocurrent is acquired using a 50 Ω-6 dB attenuator load, fed into a FEMTO-DUPVA GHz amplifier and visualized on either a Tektronix 350 MHz oscilloscope or a 12 GHz sampling oscilloscope (PicoScope) depending of the desired bandwith.

GHz time-resolved measurements at 355 nm

1 ns, 70 µJ pulses at a repetition rate of 100 Hz are produced by a Crylas FTSS 355-80 laser. The beam is separated to illuminate both a photodiode (trigger signal) and the sample. The sample (on PET/ITO substrate) is kept under vacuum and connected to a Keithley 2634b source-meter. A bias of 10 V is applied and the signal is acquired through a 50 Ω load on an oscilloscope (Rohde & Schwarz, RTE 1102).

kHz photoresponse measurements

The sample is connected in a cryostat and biased (1 V) using a Keithley 2634b source-meter. Illumination is either provided by a 4.4 µm QCL laser, a 1550 nm laser diode (Thorlabs FPL1055T) or a 808 nm laser diode (OdicForce RLD808300). The light beam is mechanically chopped using a Thorlabs MC2000B optical-chopper with MC1F10 blade set to 1 kHz. Current from the sample is amplified using a FEMTO DLCPA-200 current amplifier with matched bandwidth and fed into a 350 MHz oscilloscope. Beam powers, beam sizes, transparency of cryostat window as well as relative absorptions are accounted for in the presented data.

Photocurrent measurements from DC to GHz

The sample is connected in a cryostat, biased (1 V) by a Keithley 2634b and illumination is provided by one of the three lasers. For MIR QCL, frequency is set by optically chopping the beam between 1 Hz and 1 kHz and triggering on single pulses for frequencies above 1 MHz. For laser diodes at 808 nm and 1550 nm, electrical chopping allows their modulation from 1 Hz to 40 kHz. Acquisition bandwith-matched:

-the Keithley source-meter through a labview program when the modulation is slower than 1 Hz; -an oscilloscope through a DLCPA-200 current amplifier between 1 Hz and 100 kHz; -an oscilloscope through a 50 Ω load and a FEMTO DUPVA GHz voltage amplifier above 100 kHz.

CW measurements under gate bias

The sample is connected in an open setup with a hole allowing back-side illumination of the sample through the glass substrate. Illumination is provided by a 808 nm laser. Drain and gate voltages are controlled by a 2-channels Keithley 2634a source-meter. Drain voltage is set to 100 mV and gate voltage is swept from -2 to 2 V. For each 200 meV gate voltage step, drain current is allowed to stabilize for 3 minutes and is then acquired for 10 seconds in the dark, followed by 10 s of illumination and 60 seconds of dark.

DISCUSSION

HgTe CQDs have been synthetized according to the Keuleyan's methods [START_REF] Keuleyan | Mercury Telluride Colloidal Quantum Dots: Electronic Structure, Size-Dependent Spectra, and Photocurrent Detection up to 12 Μm[END_REF][START_REF] Keuleyan | Synthesis of Colloidal HgTe Quantum Dots for Narrow Mid-IR Emission and Detection[END_REF] and present a band-edge energy at 2200 cm -1 (≈4.5 µm or 270 meV) with a cut-off at 1800 cm -1 , see Figure 1a. Such transition energy has been chosen to absorb the pulsed QCL (2250 cm -1 or 4.4 µm) which will be used to probe the band edge dynamics. Note that the IR spectrum does not reveal the presence of any longer wavelength absorption relative to intraband feature (see Figure S1 of the SI). These CQDs present a typical 12-15 nm edge size as revealed by the transmission electron microscopy, see Figure 1b. They are crystalline (see inset of Figure 1b) with a zinc blende structure. Before investigating the carrier dynamics, it is critical to further clarify their electronic spectrum and transport properties. After synthesis, CQDs are capped with insulating organic ligand (dodecanethiol, DDT). To make the CQD array conductive and strengthen the inter-dot coupling, ligand exchange is carried out by replacing dodecanethiol ligands by ethanedithiol (EDT). The film is deposited on pre-patterned Au interdigitated electrodes and an ion gel electrolyte is added as a gate, see the inset of Figure 1c for a scheme of the device. Electrolyte gating ensures a strong tunability of the carrier density, air operability [START_REF] Lhuillier | Investigating the N-and p-Type Electrolytic Charging of Colloidal Nanoplatelets[END_REF] and also allows to gate thick film (100 nm in our case) which is critical for the design of phototransistors. 18Erreur ! Signet non défini. The transfer curve (drain current vs gate bias) reveals an ambipolar behavior where both hole and electron conductions are observed, see Figure 1c. The electron mobility is nevertheless an order of magnitude higher than the one from the hole. Moreover, the charge neutrality point is clearly shifted toward negative biases (around -600 meV), which suggests an n doping. The temperature dependence of the film conductance is given in Figure 1d and follows an Arrhenius law close to room temperature, with an activation energy of 90 meV. This value is slightly lower than the half band gap value (120 meV) expected for an intrinsic semiconductor material and further suggests the lightly doped character of these CQDs. Using photoemission, conducted on the TEMPO beamline of synchrotron Soleil, we are able to reconstruct the electronic spectrum of 5 µm band edge HgTe CQDs in absolute energy scale (Figure 1e), see SI for data acquisition and processing protocol. The work function of the material has been estimated to be 4.23 eV and the Fermi level lies just below the conduction band. This observation revealed that the doping observed using transport measurement is due to electrons. The Fermi level remains nevertheless within the gap which is consistent with the lack of intraband feature in the absorption spectrum and recent observations from the literature. [START_REF] Shen | Synthesis of Nonaggregating HgTe Colloidal Quantum Dots and the Emergence of Air-Stable n-Doping[END_REF][START_REF] Chen | Reversible Electrochemistry of Mercury Chalcogenide Colloidal Quantum Dot Films[END_REF] Noise characteristics and detectivity have already been demonstrated [START_REF] Lhuillier | Thermal Properties of Mid-Infrared Colloidal Quantum Dot Detectors[END_REF] in the same kind of EDT-capped HgTe CDQs, this is why we focus on probing photoconductivity dynamics to get a deeper understanding of the material properties.

Thanks to this understanding of the electronic structure, we can now investigate the photoconductive properties of the narrow band gap HgTe while resonantly exciting the interband transistion. To do so, we use a specially designed short-pulsed (6 ns rise time) and high power (up to 100 mW) QCL operating at 4.4 µm (2200 cm -1 or 280 meV) from MirSense. The latter allows operation both in continuous wave (CW) and pulsed mode. The QCL light is shined on the sample mounted in a cryostat, see Figure 2a for a scheme of the setup. To prevent any heating of the sample and also to accurately extract the photocurrent in spite of the low signal to noise ratio, the measurement is conducted while the light is modulated by an optical chopper. We can then follow the temperature dependence of the dark and photocurrent, see Figure 2b. The dark current decreases as temperature is reduced according to the reduction of the thermally activated carriers previously observed in Figure 1d. The photocurrent shows a similar trend, with nevertheless a smaller activation energy, which we can attribute to the thermal activation of the mobility occurring in hopping transport. [START_REF] Liu | Dependence of Carrier Mobility on Nanocrystal Size and Ligand Length in PbSe Nanocrystal Solids[END_REF] Under such illumination power density (0.37 W.cm -2 ), the background limited performance (BLIP) temperature, defined as the temperature where the photocurrent equals the dark current is estimated to be 78 K. We now want to probe the dynamics of the photoresponse at high frequency and at the band-edge. The signal is acquired through a 50 Ω resistor before being amplified with a GHz-bandwidth voltage amplifier (see Figure S4 of the SI for more details). The inset of Figure 2c presents the typical photocurrent response of the HgTe CQDs film to two different pulsewidths in the MIR. The 500 ns pulse is almost perfectly imaged by the sample, with rising and falling times of 23 and 14 ns, respectively. Those values are in the range of specifications of our laser, which is supposed to have 6 ns rise/fall time. A laser-limited 20 ns pulse (see Figure 2c) is still reproduced by our detector, with the rising part of the response corresponding to the duration of the pulse. This fast photoresponse is a strinking difference with other nanocrystals based technology being able to address the 3-5µm range of wavelength. Typically HgSe nanocrystals, which rely on intraband transition present a slow photoresponse with a 3dB frequency around 50Hz. [START_REF] Lhuillier | Infrared Photodetection Based on Colloidal Quantum-Dot Films with High Mobility and Optical Absorption up to THz[END_REF][START_REF] Robin | Surface Control of Doping in Self-Doped Nanocrystals[END_REF] From this data, we can conclude that the cut-off frequency of our device is extremely high (50 MHz) even while exciting the system in the mid IR.

For the sake of comparison we also investigate the carrier dynamics while the sample is excited far above the band edge. In this case, we use a 355 nm ns-pulsed laser source with a high power density, as recently described in ref [START_REF] Martinez | Probing Charge Carrier Dynamics to Unveil the Role of Surface Ligands in HgTe Narrow Band Gap Nanocrystals[END_REF] , also see Figure S4 for a scheme of the setup. Thanks to the low repetition rate and high power density of the laser, this setup presents both a large temporal (6 orders of magnitude) and intensity range of response (>3 decades). The photoresponse of the HgTe film to such short and high energy pulse is shown in Figure 2d. At early time, there is a first rise which follows the pulse duration. The decay is then composed of two parts. Up to 10 ns, we observe an exponential decay which is followed at longer time scale (from 10 ns to 10 µs) by a power law decay.

The fast initial decay presents a characteristic time constant of 1.2 ns, This time scale is typically shorter than the hopping time which is given by

T µk eR b hop 3 2 2  
, with e the proton charge, R (≈6 nm) the nanoparticle radius, µ the mobility, kb the Boltzmann constant and T the temperature (300 K). Assuming a mobility of 10 -3 cm 2 V -1 s -1 from previous report, [START_REF] Keuleyan | Mid-Infrared HgTe Colloidal Quantum Dot Photodetectors[END_REF] we estimate the hopping time to be ≈10 ns. According to Gao et al, [START_REF] Gao | Carrier Multiplication Detected through Transient Photocurrent in Device-Grade Films of Lead Selenide Quantum Dots[END_REF][START_REF] Fidler | Electron-Hole Exchange Blockade and Memory-Less Recombination in Photoexcited Films of Colloidal Quantum Dots[END_REF] at such early time scale, only the intradot carrier density relaxation is probed. The measured currents below this hopping limit result from displacement currents due to the variations of the electrical field and the effective medium dielectric constant while the carrier density is changed. [START_REF] Jayaweera | Displacement Currents in Semiconductor Quantum Dots Embedded Dielectric Media: A Method for Room Temperature Photon Detection[END_REF] Thus this early relaxation leads to a decay time which is similar to the one expected for PL of HgTe CQD with a 5 µm cut off wavelength, while the time resolved PL is almost impossible to obtain given the quasi null PL efficiency. At longer time scale, typically after a few hopping timescale, the transport can induce some inter dot change of the carrier density and filling of the surface traps. The power law observed in the transient photocurrent is characteristic of a multiple trapping transport mechanism. [START_REF] Orenstein | Photocurrent Transient Spectroscopy: Measurement of the Density of Localized States in As2Se3[END_REF][START_REF] Orenstein | Transient Photoconductivity and Photo-Induced Optical Absorption in Amorphous Semiconductors[END_REF] We recently detailed that this regime can be used to estimate the distribution of state within the gap, given by the Urbach energy [START_REF] Guyot-Sionnest | A Mirage Study of CdSe Colloidal Quantum Dot Films, Urbach Tail, and Surface States[END_REF] (

U E ) according to the equation b T k E b U   1
where b is the exponent obtained from the power law fit of the transient photocurrent at long (>10 ns) time scale. In the case of EDT we obtain a value of 36±1 meV for the Urbach energy. It is also worth noting that the multiple trapping regime is only revealed under strong excitation and that lower power density mostly exhibit the early intradot relaxation, indicating that trap filling might be power-dependent. Thanks to this understanding we can come back to the band edge dynamics. In spite of its "high power density" the QCL source operates in low energy density compared to the UV laser (10 19 photons/s for QCL vs 10 21 photons/s for 1.6 µJ pulse of UV laser), hence we do not observe any long-lived signature of trapping but only the fast, early decay. According to Figure 2d, the multitrapping regime appears at longer time scale when the light irradiance is increased, thus the fast dynamics observed at the band edge is due to the intradot carrier recombination which is much faster than the detrapping processes. Eventually, ratio of dynamics for the two processes (recombination vs trapping) makes the usual slowering of the photoresponse resulting from trapping quite ineffective in HgTe narrow band gap nanocrystals. This suggests that the time response of the HgTe CQD film can potentially be reduced to time scales as short as ≈1 ns.

Because of their narrow band gap nature (270 meV), these HgTe CQDs are a promising platform for the investigation of MEG since it is relatively easy to excite them far above the band edge. [START_REF] Smith | Multiple Exciton Generation in Colloidal Nanocrystals[END_REF] Moreover as opposed to PbS [START_REF] Semonin | Peak External Photocurrent Quantum Efficiency Exceeding 100% via MEG in a Quantum Dot Solar Cell[END_REF][START_REF] Schaller | High Efficiency Carrier Multiplication in PbSe Nanocrystals: Implications for Solar Energy Conversion[END_REF] there are only few reports on MEG in Hg(Cd)Te QD, [START_REF] Kershaw | Multiple Exciton Generation in Cluster-Free Alloy CdxHg1-xTe Colloidal Quantum Dots Synthesized in Water[END_REF][START_REF] Al-Otaify | Multiple Exciton Generation and Ultrafast Exciton Dynamics in HgTe Colloidal Quantum Dots[END_REF] while this material may present a threshold for MEG as low as two band edge energy due to relatively large ratio of the hole mass over the electron mass. [START_REF] Kershaw | Carrier Multiplication Mechanisms and Competing Processes in Colloidal Semiconductor Nanostructures[END_REF] Here we choose to investigate the MEG effect while shining laser sources at the 1.03 x EG (QCL at λ=4.4 µm), ≈3 x EG (laser diode at λ=1.55 µm) and 5.7 x EG (laser diode at λ=808 nm), EG being the band edge energy. Figure 3a gives a scheme of the setup with the three different sources. Because the experimental observation of MEG has led to a lot of controversy in the past, [START_REF] Kershaw | Carrier Multiplication Mechanisms and Competing Processes in Colloidal Semiconductor Nanostructures[END_REF] we have carefully checked several points. First, the measurements are conducted at low pumping fluence. Indeed, considering an absorption cross section per QD 49 of σQD = 6x10 -15 cm² at 5 µm, we can write the number of excitons per QD as 𝑛 𝑒𝑥 = 𝜎 𝑄𝐷 • 𝜙 • 𝜏 𝑒𝑥𝑐 with 𝜙 the incident photon flux and 𝜏 𝑒𝑥 the exciton lifetime. Taking a value of 10 19 s -1 cm -2 for the photon flux and a conservative assumption of 10 ns for the lifetime, we get 𝑛 𝑒𝑥 = 6𝑥10 -5 exciton/QD, far below 1. We can hence rule out any effect of multi-excitons injection in this regime. Moreover, measurements are conducted with modulated light in a lock-in detection configuration, and in particular DC measurements will be excluded because they include some drift of the signal due to heating. Finally using frequency resolved measurements, we check that the responsivity of our device is frequency independent over a broad range (10 Hz-10 kHz). We can thus exclude that the difference of behavior with photon energy may result from frequency dependence of the signal. Moreover the flatness of the photoresponse with frequency (see Figure 3c) is of utmost interest for the future use of the material for photodetection since it limits the drift and potential needs for a two point recalibration. 𝜙 . We would like to point that we do not present here absolute values for intrinsic efficiencies, as everything is normalized to the value measured for illumination at 4.4 µm. Figure 3b presents the evolution of the relative gain 𝑔 𝜆 /𝑔 𝑀𝐼𝑅 with photon flux for the three different wavelengths. In this experiment, all lasers are optically chopped at 1 kHz and the photon flux is changed by adjusting the beam power. It appears that illuminations at 4400 nm and 1550 nm have very similar efficiencies, when the 808 nm illumination shows a 3 to 4 times higher efficiency. We have here a manifestation of the MEG effect, with a photon energy threshold of at least 3 x EG since this effect is barely observed for 1550 nm illumination. This value is slightly above the value of 2.5 x EG determined by spectroscopy means on more confined HgTe QDs by Al-Otaify et al. [START_REF] Al-Otaify | Multiple Exciton Generation and Ultrafast Exciton Dynamics in HgTe Colloidal Quantum Dots[END_REF] Our observation consequently also suggests that many reports of the quantum efficiency and photoresponse of device based on narrow band gap CQD and probed with wavelength far above the band edge may overestimate the final device performance in the mid-IR.

In the last section of this paper, we investigate the tunability of the photoresponse under Fermi level control as a path to tune the majority carrier density [START_REF] Lhuillier | Electrolyte-Gated Colloidal Nanoplatelets-Based Phototransistor and Its Use for Bicolor Detection[END_REF][START_REF] Liu | N-and p-Type HgTe Quantum Dot Films[END_REF][START_REF] Livache | Charge Dynamics and Optolectronic Properties in HgTe Colloidal Quantum Wells[END_REF] and a way to reduce dark current. [START_REF] Chen | Mercury Telluride Quantum Dot Based Phototransistor Enabling High-Sensitivity Room-Temperature Photodetection at 2000 Nm[END_REF] A scheme of the setup is given in Figure 4a. As the gate bias is applied, see Figure 4b, not only the magnitude of the response can be tuned but even its sign. Overall positive photoresponse is obtained under hole injection (negative gate bias), while the photoresponse turns negative under electron injection (positive gate bias), see Figure 4b andc. Such negative photoresponse has already been observed in CQDs film, [START_REF] Liu | III-V Nanocrystals Capped with Molecular Metal Chalcogenide Ligands: High Electron Mobility and Ambipolar Photoresponse[END_REF] Si nanowires [START_REF] Baek | Negative Photoconductance in Heavily Doped Si Nanowire Field-Effect Transistors[END_REF] or Van der Waals heterostructures [START_REF] Henck | Electrolytic Phototransistor Based on Graphene-MoS2 van Der Waals p-n Heterojunction with Tunable Photoresponse[END_REF] and explained by Rose. 54 To clarify this observation we propose the following model. Let us consider that the current density through our films can be written 𝑗 = 𝑒(𝑛 𝑒 𝜇 𝑒 + 𝑛 ℎ 𝜇 ℎ )𝐸, with ne, µe, nh, µh the electrons (resp. holes) densities and mobilities in the conduction band (resp. valence band), e the elementary charge and E the applied drain source electric field. Our system is initially electron-rich (Figure 1e), so we can set the hole density to 0 as long as we do not consider too negative gate biases. Under hole injection, since the Fermi level is more deeply within the band gap, we have 𝑛 𝑑𝑎𝑟𝑘 + Δ𝑛 𝑔𝑎𝑡𝑒 ≈ 0, making this regime the most interesting for photodetection. The light illumination induces a strong change of the carrier density leading to a strong positive photoresponse. Because of the ambipolar behavior of our material, dark current also increases under hole injection and the Ilight/Idark ratio shows a maximum value around a gate bias of -600 mV (see Figure S7). It is interesting to note that this value corresponds to the charge neutrality point determined in Figure 1c, and that it gives us information about the leverage we get using this electrolytic gate. Assuming that this gate bias corresponds to the point where the Fermi level lies in the middle of the gap and knowing from Figure 1e that there is 120 meV between the Fermi level at zero gate bias and the middle of the gap, we get a value of Δ𝐸 𝐹 Δ𝑉 𝐺𝑆 = 0.2. While this value is smaller than the value of 1 obtained using a four electrodes electrochemistry setup, it still enables the probing of large energy scales with small applied voltages.

Under electron injection though, the Fermi level is within the conduction band and the nanocrystals get degenerately doped. The electron density is large and set by the gate rather than by the light. This leads to 𝑛 𝑒 = 𝑛 𝑑𝑎𝑟𝑘 + Δ𝑛 𝑔𝑎𝑡𝑒 + Δ𝑛 𝑙𝑖𝑔ℎ𝑡 ≈ Δ𝑛 𝑔𝑎𝑡𝑒 . For each electron injected in the conduction band, there is a hole in the valence band that will act as a recombination center for all the electrons of the CB. As a result, the overall electron mobility in the conduction band is lower under illumination than in the dark. Hence we have 𝜇 𝑙𝑖𝑔ℎ𝑡 < 𝜇 𝑑𝑎𝑟𝑘 . Consequently we have in the dark, 𝑗 𝑑𝑎𝑟𝑘 = 𝑒Δ𝑛 𝑔𝑎𝑡𝑒 𝜇 𝑑𝑎𝑟𝑘 𝐸 and under illumination 𝑗 𝑙𝑖𝑔ℎ𝑡 = 𝑒(Δ𝑛 𝑔𝑎𝑡𝑒 + Δ𝑛 𝑙𝑖𝑔ℎ𝑡 )𝜇 𝑙𝑖𝑔ℎ𝑡 𝐸 ≈ 𝑒Δ𝑛 𝑔𝑎𝑡𝑒 𝜇 𝑙𝑖𝑔ℎ𝑡 𝐸 < 𝑗 𝑑𝑎𝑟𝑘 . The drop of mobility is no longer compensated by the increase in carrier density, so we observe a negative photocurrent.

CONCLUSION

We have investigated the dynamics of band-edge illumination in films of HgTe QDs with absorption in the MIR. We are able to see a current modulation under illumination with very high dynamics, and we claim that our devices are capable of MIR detection with a large bandwidth (above 10 MHz). We believe that those fast dynamics are the result of the ambipolar behavior of our material, as well as reduced role played by the traps under low power illumination. As a result, photoresponse in our system mainly results from recombination-limited processes and mostly reflects instantaneous carrier density changes. We presented evidences for multi-exciton generation detected through photocurrent measurements in our devices, with a threshold around 3 EG and an efficiency of 3 to 4 (compared to efficiency in the MIR) at 6 EG. This MEG effect seems to be robust on a large frequency range, reinforcing our claim for high-bandwidth device. To conclude, we investigated the effect of gate on photoconduction and showed that photoresponse can be switched from positive to negative under hole or electron injection, respectively. We explain this effect with a simple model where carrier density is set by the light under hole injection, and by the gate under electron injection. Mobility reduction under illumination (because of the introduction of recombination centers) then explains why negative photoconduction arises.

TOC FIGURE

24

 24

Figure 1 :

 1 Figure 1: Physical properties of HgTe QDs used in this work. a. FTIR spectrum of EDT-capped HgTe QDs assembled into a film on CaF2 substrate. Colored lines indicate the energy of two IR laser sources used in the work. b. TEM image of HgTe QDs. Inset: High-resolution TEM image of a single QD. c. Transfer curve (drain current as a function of gate bias) of EDT-capped HgTe QDs sample using electrolytic gating. The curve shows ambipolar behavior. Inset: scheme of the FET device. d. Cooling curve of an EDT-capped HgTe QDs sample under 1V bias. The Arrhenius fit gives a value of 90 meV for activation energy. e. Energy levels of HgTe QDs determined using XPS, with Urbach tails describing the trap distributions.

Figure 2 :

 2 Figure 2: a. Scheme of the measurement setup with a mid-infrared QCL. b. Evolution of the current in the dark and under MIR illumination as the sample is cooled. Inset: evolution of the modulation with temperature. c. Typical sample response to a laser-limited 20 ns QCL pulse in the MIR. Inset: response to a 500 ns QCL pulse allowing the extraction of rise and fall time constants of the sample: trise = 23 ns and tfall = 15 ns. QCL power is 0.6 W/cm² and bias is 9 V. d. Sample response to a 1 ns, high energy pulse in the UV (355 nm), as a function of optical power. The two components are fitted to extract recombination time and Urbach energy.

Figure 3 :

 3 Figure 3: Multi-exciton generation in EDT-capped HgTe QD films. a. Scheme of the high-bandwidth measurement setup using alternatively three different laser sources ranging from NIR to MIR. Acquisition can be changed to be bandwidth-matched. b. Relative gain 𝒈 = 𝑰 𝒑𝒉 /𝜼𝒆𝝓 𝟎 (expression is described in text) as a function of photon flux for the three different wavelengths. For the three lasers, the beam is chopped at 1 kHz using an optical chopper and the sample is biased at 1 V. c. Frequency dependence of the relative gain for the three wavelengths. Frequency ranges from DC to 10 MHz and response is measured with bandwidth-matched acquisition setup. Sample bias is 1 V and the experiment is conducted at room-temperature.

Figure 4 :

 4 Figure 4: Negative photocurrent behavior under gate bias. a. Scheme of the experiment: the sample with an electrolytic gate is illuminated from the back with an 808 nm laser. b. Photocurrent response of the sample to a 10 s light pulse as a function of gate bias. Drain bias is set to 100 mV and gate bias is swept from -1 V to 1 V. c. Reconstructed transfer curve (channel current as a function of gate bias) and photocurrent maximum intensity as a function of gate bias.

ACKNOWLEDEGMENTS

EL thanks the support ERC starting grant blackQD (grant project 756225). We acknowledge the use of clean-room facilities from the "Centrale de Proximité Paris-Centre". This work has been supported by the Region Ile-de-France in the framework of DIM Nano-K (grant dopQD). This work was supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, and more specifically within the framework of the Cluster of Excellence MATISSE, as well as by the grants Nanodose and H2DH.

SUPPORTING INFORMATION

Absorption spectra and X-ray diffraction diagram of the material, XPS measurement information, measurement setups for high-bandwitdh time-resolved experiment, additional data for temperature-dependent photocurrent, MEG and gate-controlled phototransport.


Scheme 2. Synthesis Plan for NVS-SM2 (1)

Our synthesis commenced with a palladium-catalyzed borylation 3 of iodide 2 that afforded a mixture (90:10) of boronates 3 and 3', which was directly used in a Suzuki-Miyaura coupling with iodopyridazine 4 to furnish adduct 5 (Scheme 3). 4 Initial attempts to perform this reaction using Fu's condition 5,6 did not yield the expected adduct 5 (entry 1, Table 1). Switching to other catalytic systems using S-Phos, X-Phos or PPh 3 as ligands provided the desired adduct with a conversion of 20-32% (entries 2-4). Ultimately, the air and moisture stable PdCl 2 (dppf) proved to be particularly effective (entry 5). Finally, several other combinations of solvent and base were examined, and when the reaction was carried out in dioxane/H 2 O with the use of K 3 PO 4 as a base, a 70% yield could be achieved (entry 8). This preference for K + as a counteraction of the base suggests that this Suzuki coupling involves a fast oxidation step and a rate-determining transmetalation. 7 Further continuation of the synthesis required the replacement of the methoxy by a benzyloxy that can be efficiently deprotected in the final step. Indeed, Novartis scientists reported in their patent that the demethylation at a latter step is performed with a 13% yield only. 2 Thus, demethylation with boron trichloride of 5, followed by benzylation, gave the requisite intermediate 7 in a 98% yield. With the intermediate 7 in hand, we proceeded to its coupling with the pyrazolylboronate moiety. Original attempts to perform this reaction using a pyrazolylboronate protected with a Boc were not satisfactory, due to the lability of the Boc in the examined conditions. To circumvent this issue, we incorporated a Trityl protecting group onto the pyrazolylboronate. This reagent was conveniently prepared in 3 steps from pyrazole 8 (Scheme 4). After extensive studies, we found that arylbromide 7 can be coupled in the presence of Pd(PPh 3 ) 4 with boronate 11 to prepare adduct 12 in a 30% yield (entries 3-4, Table 2). Initial attempts to use unprotected pyrazole-4-boronic acid did not deliver the expected adducts. When we examined this reaction with the reactant protected as a Boc, the yield was not reproducible and lied between 0 and 20%.

Scheme 3. Synthesis of Intermediate 7

Scheme 4. Preparation of Tritylpyrazolylboronate 11

To improve this reaction condition, we examined the coupling of 11 with 3-bromoanisole 13 using Pd(PPh 3 ) 4 , Na 2 CO 3 in PhMe/EtOH/H 2 O. [START_REF] Yang | Aryl bromides have been shown to afford higher yield that the cognate triflates on this type of substrates[END_REF] Our initial assay afforded the expected adduct in a 33% yield (entry 1, Table 3). Increasing the amount of boronate 11 did not modify the yield (entry 2). Gratefully, doubling the amount of catalyst improved the yield up to 70% (entry 3), suggesting that the catalyst is unstable in this condition.

With an optimized Suzuki-Miyaura coupling of boronate 11 in hand, an efficient route to synthesize advanced intermediate 16 was developed (Scheme 5). First, the iminochloride 7 was treated with anhydrous tetramethylammonium fluoride under Sanford's condition 9 to smoothly furnish fluoropyridazine 15, in 98% yield. The latter has two main advantages compared to the cognate chloropyridazine 7: the iminofluoride moiety is resistant to Suzuki coupling, and importantly, it is much more reactive in SNAr reactions. The coupling of boronate 11 with 15 delivered adduct 16 in 53% yield.

Scheme 5. Synthesis of advanced intermediate

The synthesis of diamine 18 was conveniently achieved by formylation of 17 with ethyl formate and reduction of the obtained formamide with LiAlH 4 . Its condensation with fluoropyridazine 16 gave aminopyridazine 19 in a satisfactory yield (56%) (Scheme 6). We originally considered performing this reaction with a chloropyridazine, but all of our attempts failed to deliver the expected adduct. Completion of the synthesis was accomplished by a double deprotection of the phenol and pyrazole moieties with a 94% yield for both steps.

Scheme 6. Endgame of the Synthesis

In conclusion, the synthesis of NVS-SM2 has been accomplished in 9 linear steps with an overall yield of 14% (average yield: 82%). It involves few more steps that the original one, however we optimized all the steps and some of them can be carried a very convenient manner with a near quantitative yield. For example, the conversion of 5 into 7 was performed in 2 steps with an overall yield of 98% and the intermediate of this sequence was directly used in the second step without purification. Actually, this sequence can be easily achieved in half a day. The fluoridation (7 → 15) and deprotection (19 → 20 → 1) steps are also performed in high yield in a very expedient manner.

Thus, this route can satisfy the global demand for NVS-SM2 to examine in detail its therapeutic potential to treat SMA and other diseases associated with alterations in RNA splicing. In addition, the efficacy of the synthesis reported herein offers an opportunity to explore further the pharmacological effects of chemical modifications in the structure of NVS-SM2.

■ EXPERIMENTAL SECTION

All commercial reagents were used without purification. All the anhydrous solvents used are commercial or are conserved on molecular sieves. All reactions sensitive to moisture or oxygen were carried out under argon atmosphere and in flasks dried at 110 °C. Reactions were stirred with a magnetic stirrer. Temperatures for the reactions refer to bath temperatures. Reactions were monitored by TLC (0.2 mm, Merck DC Platten Kieselgel 60 F 254 ) with detection by UV light (λ = 254 nm) and treatment with anisaldehyde and potassium permanganate-stain. Melting points were recorded on an Electrothermal melting point apparatus and are uncorrected.

NMR spectras were acquired on a Bruker DRX-400 spectrometer in CDCl 3 (referenced to 7.26 ppm for 1H and 77.0 ppm for 13 C), (CD 3 ) 2 SO (referenced to 2.50 ppm for 1 H and 39.5 ppm for 13 C) or CD 3 OD (referenced to 3.31 ppm for 1 H and 49 ppm for 13 C) as solvents. Coupling constants (J) are in Hz. Chemical shifts are reported in parts per million (ppm). The multiplicities of the signals are described using the following abbreviations: s = singlet, d = doublet, t = triplet, m = multiplet. High resolution mass spectra were recorded on a Bruker MicroTOF-Q (ESI Q-TOF) spectrometer.

3-(4-Bromo-2-methoxyphenyl)-6-chloropyridazine (5)

1,1'-Bis(diphenylphosphinoferrocene)-palladium (II) dichloride CH 2 Cl 2 complex (574 mg, 0.70 mmol) was added to a dioxane (19 mL) / H 2 O (1 mL) solution of iodopyridazine 4 (1.86 g, 7.73 mmol), boronates (3, 3') (2.2 g, 7.03 mmol) and potassium phosphate (4.48 g, 21.08 mmol) at room temperature under argon atmosphere (the flask was evacuated and refilled with argon five times before adding of Pd complex). The reaction was heated at 90 °C for 16h. After cooling to room temperature, the reaction mixture was diluted with EtOAc (50 mL), filtered through celite with copious washings, and then concentrated. The organic layer was washed with water, brine, dried over anhydrous MgSO 4 , filtered, concentrated and purified by column chromatography on silica gel using DCM (100%) as eluent to give 5 (1.63

5-Bromo-2-(6-chloropyridazin-3-yl)phenol (6)

To a stirred solution of 5 (500 mg, 1.67 mmol) in dry DCM (50 mL), BCl 3 (5 mL, 5 mmol, 1M in DCM) was added dropwise at 0 °C under argon atmosphere. The resulting reaction mixture was stirred over 3h at room temperature then quenched with water. The aqueous layer was extracted with DCM (2 × 50 mL). Combined organic layers were washed with brine, dried over anhydrous MgSO 4 , filtered, and concentrated to give 6 (470 mg, 99%) as a pale-yellow solid which was used without further purification ; mp = 161-164 °C ;

3-[2-(Benzyloxy)-4-bromophenyl]-6-chloropyridazine (7)

To a stirred solution of phenol 6 (130 mg, 0.45 mmol) in dry DMF (1.5 mL), was added potassium carbonate (126 mg, 0.9 mmol) and then benzyl bromide (86 mg, 0.5 mmol) at room temperature under argon atmosphere. The resulting reaction mixture was stirred over 10 min at the same temperature and then diluted with DCM (15 mL). The organic layer was washed with water, dried over anhydrous MgSO 4 , filtered and concentrated to give chloropyridazine 7 (167 mg, 98%) as a white solid which was used without further purification ; mp = 177-180 °C ;

4-(4,4,5,5-Tetramethyl-1,3,2-dioxaborolan-2-yl)-1-trityl-1H-pyrazole (11)

To a stirred solution of 4-bromo-tritylpyrazole 10 (2 g, 5.14 mmol) and bis(pinacolato)diboron (1.44 g, 5.65 mmol) in DMF(14 ml), was added 1,1'-bis(diphenylphosphinoferrocene)-palladium (II) dichloride CH 2 Cl 2 complex (420 mg, 0.51 mmol) and potassium acetate (1.51g, 15.42 mmol) at room temperature under argon atmosphere. The resulting mixture was heated at 80 °C for 16h. After cooling to room temperature, the reaction mixture was diluted with DCM (50 mL). The organic layer was washed with water, brine, dried over anhydrous MgSO 4 , filtered, concentrated and purified by column chromatography on silica gel using pentane / Et 2 O (10/0 to 8/2) as eluent to give boronate 11 (

3-(2-(Benzyloxy)-4-(1-trityl-1H-pyrazol-4-yl)phenyl)-6chloropyridazine (12)

Pd(PPh 3 ) 4 (31 mg, 0.027 mmol) was added to a stirred solution of chloropyridazine 7 (100 mg, 0.27 mmol), boronate 11 (174 mg, 0.40 mmol) and Na 2 CO 3 (117 mg, 0.53 mmol) in PhMe (3 ml) / EtOH (0.3 ml) / H 2 O (0.3 ml) at room temperature under argon atmosphere (the flask was purged five times with argon before adding the Pd complex). The resultant mixture was stirred at the same temperature for 5 min and then at 110 °C for 18h. After cooling to room temperature, the reaction mixture was diluted with EtOAc (25 mL). The organic layer was washed with water, brine, dried over MgSO 4 , concentrated and purified by column chromatography on silica gel using pentane / Et 2 O (8/2 to 5/5) as eluent to give chloropyridazine 12 (50 mg, 30%) as a white solid ; mp = 216-219 °C ; 1 H NMR (400 MHz, CDCl 3 ): δ 5.07 (2H, s), 7.05 (1H, d, J = 0.9 Hz),

4-(3-Methoxyphenyl)-1-trityl-1H-pyrazole (14)

The title compound was prepared similarly to the synthesis of chloropyridazine 12 starting from 3-bromoanisole 13 (80 mg, 0.054 mmol), boronate 11 (281 mg, 0.64 mmol), sodium carbonate (91 mg, 0.86 mmol), Pd(PPh 3 ) 4 (100 mg, 0.086 mmol) and PhMe (3 ml) / EtOH (0.3 ml) / H 2 O (0.3 ml). The crude product was purified by chromatography on silica gel using pentane / Et 2 O (10/0 to 80/20) as eluent to give pyridazine 14 (126 mg, 70%) as a white solid ; mp = 120-123 °C ;

3-[2-(Benzyloxy)-4-bromophenyl]-6-fluoropyridazine (15)

To a stirred solution of chloropyridazine 7 (750 mg, 1.99 mmol) in dry DMF (12 mL), anhydrous NMe 4 F (375 mg, 3.98 mmol) was added at room temperature under argon atmosphere. The resulting reaction mixture was stirred at the same temperature for 24h before it was diluted with DCM (70 mL). The organic layer was washed with water (3 × 120 mL), brine (1 × 100 mL), dried over anhydrous MgSO 4 , filtered and concentrated to give fluoropyridazine 15 (700 mg, 98%) as a white solid which was used without further purification ; mp = 167-170 °C ; 1 H NMR (400 MHz, CDCl 3 ): δ 5.12 (2H, s), 7.13 (1H, dd, J =1.5, 9.2 Hz), 7.27-7.40 (7H, m), 7.8 (1H, d, J = 8.2 Hz), 8.12 (1H, dd, J = 7.5, 8.

3-[2-(Benzyloxy)-4-(1-trityl-1H-pyrazol-4-yl)phenyl]-6fluoropyridazine (16)

The title compound was prepared similarly to the synthesis of chloropyridazine 12 starting from fluoropyridazine 15 (200 mg, 0.55 mmol), boronate 11 (364 mg, 0.83 mmol), sodium carbonate (117 mg, 1.1 mmol), Pd(PPh 3 ) 4 (129 mg, 0.11 mmol) and PhMe (5 ml) / EtOH (0.5 ml) / H 2 O (0.5 ml). The crude product was purified by chromatography on silica gel using pentane / Et 2 O (8/2 to 5/5) as eluent to give fluoropyridazine 16 (172 mg, 53%) as a white solid ; mp = 203-206 °C ; 1 H NMR (400 MHz, CDCl 3 ): δ 5.19 (2H, s), 7.13 (1H, dd, J = 1.5, 9.2 Hz), 7.18 (7H, d, J = 1.5 Hz), 7.22 (1H, d, J = 8.3 Hz), 7.24-7.3 (6H, m), 7.32-7.43 (14H, m), 7.73 (1H, s), 7.99 (1H, dd, J = 1.4, 8.2 Hz), 8.00 (1H, s), 8.21 (1H, dd, J = 7.5, 8.

N,2,2,6,6-pentamethylpiperidin-4-amine (18)

A solution of 17 (4.4 mL, 0.026 mmol) in ethyl formate (6.5 mL, 0.078 mmol) was heated at 65 °C for 4-5 h. The resulting thick, white suspension was cooled to room temperature and filtered. After the filter cake was washed with EtOAc (20 mL), the solid was dried under vacuum to give 3.8 g (79 % yield) of N- (2,2,6,6-tetramethylpiperidin-4-yl)formamide, which was used directly in the next step. A 250 mL round bottom flask equipped with a large Teflon-coated stir bar was charged with LiAlH 4 (1.17 g, 31 mmol), fitted with a reflux condenser, and purged with argon. THF (40 mL) was added and the resulting suspension was cooled to 0 °C. A N- (2,2,6,6-tetramethylpiperidin-4-yl)formamide (3.8 g, 20.6 mmol) was added in portion over 10 min (CAUTION: hydrogen gas evolution!). The cooling bath was replaced with an oil bath and the colorless solution was heated at 65 °C for 24h under a slow stream of argon. The resulting white suspension was cooled to 0 °C and then carefully quenched by dropwise addition of water (10 mL; CAUTION: violently exothermic reaction, evolution of hydrogen gas!) followed by a 20% aq NaOH solution (20 mL). The resulting suspension was stirred at room temperature for 15 min. MeOH (40 mL) was added then the mixture was filtered on celite. The filtrate was concentrated and then the residue was dissolved with EtOAc (50 mL). The organic layer was washed with water, brine, dried over anhydrous MgSO 4 , filtered and concentrated to give diamine 18 (3.25 g, 93%) as a yellow liquid which was used without further purification ; 1 H NMR (400 MHz, (CD 3 ) 2 SO): δ 0.72 (2H, t, J = 11.8 Hz), 1.00 (6H, s), 1.09 (6H, s), 1.68 (2H, dd, J = 3.4, 12.3 Hz), 2.26 (3H, s), 2.6 (1H, tdd, J = 3.5, 11.5, 11.5 Hz) ; 13 C NMR (100 MHz, (CD 3 ) 2 SO): δ 28.

6-[2-(Benzyloxy)-4-(1-trityl-1H-pyrazol-4-yl)phenyl]-Nmethyl-N-(2,2,6,6-tetramethylpiperidin-4-yl)pyridazin-3amine (19)

To a stirred solution of 16 (230 mg, 0.39 mmol) in butan-1-ol (4 ml), diamine 18 (133 mg, 0.78 mmol) was added at room temperature under argon atmosphere. The mixture was heated at 120 °C for 48h. After cooling to room temperature, butan-1ol was removed using rotary evaporator, then the residue was diluted with DCM (50 mL). The organic layer was washed with water, dried over anhydrous MgSO 4 , filtered, concentrated and purified by flash chromatography on silica gel using DCM / MeOH (10/0 to 8/2) as eluent to give 19 (160 mg, 56%) as a yellow solid ; mp = 105-108 °C ;

2-[6-[Methyl(2,2,6,6-tetramethylpiperidin-4yl)amino]pyridazin-3-yl]-5-(1-trityl-1H-pyrazol-4yl)phenol (20)

To a stirred solution of 19 (110 mg, 0.15 mmol) in MeOH (7 ml), catalytic amount of 10% palladium on carbon was added under H 2 atmosphere. The mixture was stirred for 48h at room temperature and then filtered on celite. The filtrate was concentrated and purified by flash chromatography on silica gel using DCM / MeOH (10/0 to 8/2) as eluent to give phenol 20 (90 mg, 94%) as a yellow solid ; mp = 132-135 °C ; To a stirred solution of 20 (80 mg, 0.12 mmol) in THF (2 ml) / MeOH (2 ml), 2 ml of HCl (6M) was added at room temperature. The mixture was stirred at the same temperature. After 3h, solvents were removed using rotary evaporator. The yellow product obtained in salt form was dissolved in DCM / MeOH (50/50) and neutralized with addition of solid NaHCO 3 . Then the mixture was filtered through celite. The filtrate was concentrated and purified by flash chromatography using DCM / MeOH (10/0 to 8/2) as eluent to give NVS-SM2 (1) (48 mg, quant.) as a yellow solid ; mp = 146-149 °C ;

  1 H NMR (400 MHz, CDCl 3 ): δ 7.10 (1H, dd, J = 1.5, 8.5 Hz), 7.29 (1H, d, J = 1.5 Hz), 7.52 (1H, d, J = 8.5 Hz), 7.67 (1H, d, J = 9.3 Hz), 8.01 (1H, d, J = 9.3 Hz) ; 13 C NMR (100 MHz, CDCl 3 ): δ 114.9, 122.4, 122.9, 125.7, 127.1, 127.5, 130.1, 155.0, 159.5, 160.5 ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 10 H 7 BrClN 2 O 284.9425 ; found 284.9420.

  2 Hz) ; 13 C NMR (100 MHz, CDCl 3 ): δ 71.3, 114.7 (d, J = 33 Hz), 116.5, 124.2, 125.1, 125.2, 127.5, 128.6, 128.9, 132.5, 133.7 (d, J = 7 Hz), 135.6, 156.7, 157.6 (d, J = 2.7 Hz), 165.7 (d, J = 245 Hz) ; 19 F NMR decoupled 1 H (376 MHz, CDCl 3 ): -81.27 (1F, s) ; 19 F NMR coupled 1 H (376 MHz, CDCl 3 ): -81.27 (1F, d, J = 7.5 Hz) ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 17 H 13 BrFN 2 O 359.0190 ; found 359.0192.

  3 Hz) ; 13 C NMR (100 MHz, CDCl 3 ): δ 71.1, 79.1, 110.2, 114.5 (d, J = 33 Hz), 119.1, 121.0, 123.1, 127.4, 127.9, 128.0, 128.3, 128.7, 129.5, 130.2, 131.8, 133.6 (d, J = 6.8 Hz), 136.1, 132.3, 137.5, 143.0, 156.6, 158.1 (d, J = 2.5 Hz), 165 (d, J = 244 Hz) ; 19 F NMR decoupled 1 H (376 MHz, CDCl 3 ): -81.99 ; 19 F NMR coupled 1 H (376 MHz, CDCl 3 ): -81.99 (dd, J = 1.4, 7.5 Hz) ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 39 H 29 FN 4 O 589.2398 ; found 589.2395.

Table 1 . Optimization of the First Suzuki-Miyaura Cou- pling

 1

	entry	cat.	base (eq)	solvent	T °C	yield (%)
	1	Pd2(dba)3 (2 mol%)	KF	THF	80	trace
		P(tBu)3 (3 mol%)	(3)
	2	Pd(OAc)2 (10 mol%)	K2CO3	ACN/H2O	110	20
		S-Phos (20 mol%)	(2.2)
	3	Pd(OAc)2 (10mol%)	K3PO4	n-BuOH/H2O	110	21
		X-Phos (12 mol%)	(2)
	4	Pd(PPh3)4 (5 mol%) Na2CO3	EtOH/toluene/	reflux	32
			(2)	H2O
	5	PdCl2(dppf)•CH2Cl2	Na2CO3	DMF/H2O	100	40
		(10 mol%)	(2)
	6	PdCl2(dppf)•CH2Cl2	CsF	DMF/H2O	100	17
		(10 mol%)	(0.5)
	7	PdCl2(dppf)•CH2Cl2	Na2CO3	THF/ACN/H2O	100	12
		(10 mol%)	(2)
	8	PdCl2(dppf)•CH2Cl2	K3PO4	dioxane/H2O	90	70
		(10 mol%)	(3)

Table 2 . Optimization of the Second Suzuki-Miyaura Cou- pling

 2

	entry	cat.	base (eq)	solvent	T°C	yield (%)
	1	Pd2(dba)3 (3 mol%) P(tBu)3 (7 mol%)	KF (3.3)	THF	70	0
	2	Pd2(dba)3 (1 mol%) PCy3 (2.4 mol%)	K3PO4 (1.7)	dioxane/H2O	100	0
	3	Pd(PPh3)4 (10 mol%)	Na2CO3 (2)	DME/H2O (6/3)	MW 150	28
	4	Pd(PPh3)4 (10 mol%)	Na2CO3 (2)	PhMe/EtOH/H2O (10/1/1)	110

Table 3 . Optimization of second Suzuki-Miyaura using 3- bromoanisole 13 as a substrate

 3

	entry	11 (eq)	Pd(PPh3)4 (mol%)	yield (%)
	1	1.5	10	33
	2	3	10	28
	3	1.5	20	70

  g, 70%) as a white solid ; mp = 133-136 °C ; 1 H NMR (400 MHz, CDCl 3 ) δ 3.87 (3H, s), 7.16 (1H, d, J = 1.4 Hz), 7.26 (1H, dd, J = 1.4, 8.3 Hz), 7.49 (1H, d, J = 9 Hz), 7.84 (1H, d, J = 8.3 Hz), 7.98 (1H, d, J = 9 Hz) ; 13 C NMR (100 MHz, CDCl 3 ) δ 56.0, 115.0, 123.6, 124.6, 125.4, 127.2, 130.3, 132.2, 155.1, 157.1, 157.6 ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 11 H 9 BrClN 2 O 298.9581 ; found 298.9571.

  1 H NMR (400 MHz, CDCl 3 ): δ 5.12 (2H, s), 7.27-741 (8H, m), 7.89 (1H, d, J = 8.3 Hz), 7.98 (1H, d, J = 9 Hz) ; 13 C NMR (100 MHz, CDCl 3 ): δ 71.4, 116.6, 124.1, 125.1, 125.4, 127.2, 127.5, 128.6, 128.9, 130.4, 132.5, 135.6, 155.2, 156.9, 157.1 ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 17 H 13 BrClN 2 O 374.9894 ; found 374.9883.

  1 H NMR (400 MHz, CDCl 3 ): δ 3.82 (3H, s), 6.75 (1H, ddd, J = 1.0, 2.6, 8.4 Hz), 7.96 (1H, dd, J = 1.4, 2.6 Hz), 7.03 (1H, ddd, J = 1, 1.4, 7.7 Hz), 7.20-7.25 (7H, m), 7.30-7.35 (9H, m), 7.61 (1H, d, J = 0.8 Hz), 7.93 (1H, d, J = 0.8 Hz) ; 13 C NMR (100 MHz, CDCl 3 ): δ 55.3, 78.9, 111.4, 111.6, 118.2, 121.5, 127.8, 127.9, 129.3, 129.8, 130.2, 134.0, 137.3, 143.1, 160.0 ; HRMS (ESI-TOF) m/z: [M+Na] + calcd for C 29 H 24 N 2 NaO 439,1786 ; found 439,1768.

  5, 32.5, 34.3, 44.5, 49.7, 50.6 ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 10 H 23 N 2 171.1856 ; found 171.1853.

  1 H NMR (400 MHz, CDCl 3 ): δ 1.18 (6H, s),1.35 (6H, s), 1.40 (2H, t, J = 12.3 Hz), 1.69 (2H, dd, J = 2, 12 Hz), 3.00 (3H, s), 4.88 (1H, m), 6.98 (1H, d, J = 9.8 Hz), 7.01 (1H, d, J = 8.1 Hz), 7.11 (1H, s), 7.16-7.23 (6H, m), 7.29-7.37 (9H, m), 7.52 (1H, d, J = 8.3 Hz), 7.66 (1H, s), 7.92 (1H, s), 7.79 (1H, d, J = 9.8 Hz), 7.98 (1H, s) ; 13 C NMR (100 MHz, CDCl 3 ): δ 28.9, 29.4, 35.3, 42.0, 48.4, 51.5, 79.1, 113.9, 114.8, 116.0, 116.8, 121.2, 124.5, 125.4, 128.0, 129.7, 130.3, 134.8, 137.5, 143.2, 151.6, 157.9, 159.4 ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 42 H 45 N 6 O 649.3649 ; found 649.3634.

  1 H NMR (400 MHz, MeOD): δ 1.22 (6H, s), 1.35 (6H, s), 1.48-1.65 (4H, m), 2.87 (3H, s), 4.98 (1H, m), 7.04-7.17 (3H, m), 7.59 (1H, d, J = 7.4 Hz), 7.89 (1H, d, J = 9.4 Hz), 7.97 (2H, s) ; 13 C NMR (100 MHz, MeOD): δ 27.5, 29.8, 33.6, 41.3, 54, 115, 116.3, 117.2, 117.6, 123, 126.4, 127.3, 136.2, 152.8, 159.2, 159.9 ; HRMS (ESI-TOF) m/z: [M+H] + calcd for C 23 H 31 N 6 O 407.2554 ; found 407.2550.

■ ACKNOWLEDGMENTS

We thank the "Ministère de l'Enseignement Supérieur et de l'Innovation" for a fellowship to H. A-H.

■ ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: Spectral data for compounds described herein (PDF)

■ AUTHOR INFORMATION Corresponding Author

*E-mail: desaubry@unistra.fr

Present Address

Laboratory of Therapeutic Innovation (UMR 7200), Faculty of Pharmacy, University of Strasbourg-CNRS, 67401, Illkirch, France

Notes

The authors declare no competing financial interest.


Cécile Appert-Rolland
email: cecile.appert-rolland@th.u-psud.fr

Julien Pettré

Anne-Hélène Olivier

William Warren

Aymeric Duigou-Majumdar

Etienne Pinsard

Alexandre Nicolas

Experimental Study of Collective Pedestrian Dynamics

Keywords: pedestrian dynamics, experiments, tracking, crossing flows, pattern formation, dense crowds

We report on two series of experiments, conducted in the frame of two different collaborations designed to study how pedestrians adapt their trajectories and velocities in groups or crowds. Strong emphasis is put on the motivations for the chosen protocols and the experimental implementation. The first series deals with pattern formation, interactions between pedestrians, and decision-making in pedestrian groups at low to medium densities. In particular, we show how pedestrians adapt their headways in single-file motion depending on the (prescribed) leader's velocity. The second series of experiments focuses on static crowds at higher densities, a situation that can be critical in real life and in which the pedestrians' choices of motion are strongly constrained sterically. More precisely, we study the crowd's response to its crossing by a pedestrian or a cylindrical obstacle of 74cm in diameter. In the latter case, for a moderately dense crowd, we observe displacements that quickly decay with the minimal distance to the obstacle, over a lengthscale of the order of the meter.

Introduction

The motion of a particle in the midst of a crowd often differs dramatically from its motion in free space [START_REF] Sentjabrskaja | Anomalous dynamics of intruders in a crowded environment of mobile obstacles[END_REF]. This is particularly true for pedestrians, who move in one or two-dimensional space, where trajectories are more likely to intersect than in three dimensions. The conflicts generated by space-sharing do not arise only because of physical constraints (which preclude overlaps, in particular), but also because of individual preferences, which render some situations unfavorable, in spite of being physically possible, for instance coming in close contact with another pedestrian or markedly deviating from one's target direction. When such conflicts arise, pedestrians effectively interact, notably to avoid collisions, in converging or intersecting flows; they also interact when a collective decision must be made. These interactions are complex and there is no ground rule to predict them. Besides, given their non-additivity, many-body interactions cannot be straightforwardly derived from simpler situations, such as encounters between two pedestrians.

Therefore, reference (empirical) data are particularly needed regarding the way pedestrians adapt their motion in crowds, in order to test models for pedestrian dynamics [START_REF] Haghani | Crowd behaviour and motion: Empirical methods[END_REF] or to assess its impact on critical infrastructure [START_REF] Bruno | From individual behaviour to an evaluation of the collective evolution of crowds along footbridges[END_REF]. Indeed, too often, these models are calibrated using only 'macroscopic' observables. To collect reference data, two competing approaches exist: passive observations of real situations (streets, shopping malls, railway stations, etc.) and controlled experiments with voluntary participants. The former approach captures the complexity of real crowds, but involves many uncontrolled parameters which complicate the interpretation of the observations. Prepared experiments, on the other hand, render the tracking of pedestrians easier, with a variety of possible devices, and allow one to control parameters such as the density and the geometry of the environment, and to repeat the same 80-1 protocol several times in order to make a statistical analysis possible. On the downside, the participants' behaviors and the composition of the crowd may be biased by the experimental conditions. Rather than competing possibilities, the two approaches thus turn out to be complementary.

In this paper, we report on two series of controlled experiments, conducted in the frame of two different collaborations and designed to study how pedestrians adapt their trajectories and velocities in groups or crowds. We will emphasize the motivations for the experimental protocols and their implementation, while deferring an exhaustive analysis of the results to a future publication.

The first series of experiments (PEDINTERACT project ) considers situations of low to intermediate densities, involving a lot of conflicting trajectories or some collective decision process. The second series (PERCE-FOULE project) focuses on crowds at high density and likens them to a deformable medium.

Scanning the interactions between pedestrians at low or intermediate densities

Even at low or intermediate densities, pedestrians must interact to coordinate their motion. First comes, of course, the constraint that the chosen trajectories do not lead to collisions. Then, in some situations, collective decisions need to be made about where to head for or what route to choose. The experiments conducted in the frame of the PEDINTERACT project are aimed at better understanding the many-body interactions between pedestrians involved in these situations. We designed several protocols, some focusing on the need to solve multiple threads of collisions, while others put the focus on collective decisions.

Description of the PEDINTERACT experiments

The collaboration involves J. Pettré (INRIA Rennes), A.-H. Olivier (M2S Rennes), W. Warren (CLPS, Brown Univ.), C. Appert-Rolland (LPT -Orsay), and their students. The experiments took place at the Immermove platform of the M2S laboratory in Rennes (France) on 30 th -31 st , March 2016, in a sport hall equipped with 26 VICON cameras. On each of the two days, 36 to 38 adult volunteers took part in the experiment. They were wearing a bike helmet carrying 4 markers detectable by the VICON motion capture system and arranged in a unique configuration. For each experimental protocol, several realizations were performed in order to allow for a statistical analysis. A post-processing stage allows to reconstruct the individual trajectories.

Protocols

Swarm behavior: At the start, participants (unaware of the purpose of the experiment) were confined in a 8x8 m 2 area. They were assigned initial heading directions making an angle of 90, 180, 270, or 360 degrees. They were then asked to walk around in the sport hall. The purpose of the experiment was to observe whether herding or correlated collective motion spontaneously emerges. Group intersections: Two groups of 20 people each were asked to "walk straight across the room and pass through another group of participants''. The groups were not constrained laterally: they could split or become porous and merge after the intersection. The initial density within each group (around 1 ped/m 2 or 0.45 ped/m 2 ) and the angle at which the groups intersect (0, 15, 30, 90, 150, 165, or 180 degrees) were varied. For each set of parameters 12 realizations were performed, during which the composition of the groups was changed 4 times. Six additional realizations of the 90 degrees crossings were conducted with 4 pillars delimiting the intersection area, to mimick the junction between two perpendicular corridors, in which case the formation of diagonal stripes was predicted and observed [START_REF] Cividini | Diagonal patterns and chevron effect in intersecting traffic flows[END_REF]. Gate passing: A gate of width 80cm or 240 cm was crossed either unidirectional by a group of 40 people or bidirectionally by 2 groups of 20 people. Besides, the influence of the initial crowd density on the heading towards the gate was studied using an even larger gate (800cm). Each situation was repeated 6 times.

Collective turning decision:

A group of 40 people, initially packed with a density of 1 or 0.45 ped/m 2 , was asked to "walk across the room, and make a left or right turn, while staying together as a group''. The instruction to turn right or left was given to the group before each realization. As there was no official group leader, a non-verbal decision had to be reached about when to turn. Sometimes a single leader 80-2 emerged, but more often a leading small subgroup took charge. An intriguing question is whether there exists a critical size for this leading subgroup above which others will automatically follow, and how followers will deal with conflicting information if two leading subgroups go in different directions. Each case (left or right turn, initial density) was repeated 5 times.

In the next section, we will present into deeper details one last protocol involving collective and individual decisions, as well as some results.

Unidimensional flow without density constraint

The last protocol focuses on unidirectional flows. Under these conditions, conflicts arise whenever the pedestrians'free velocities are not exactly equal, and induce interactions. While this situation had already been studied by several groups at fixed density and with a prescribed trajectory path [START_REF] Jelic | Properties of pedestrians walking in line: Fundamental diagrams[END_REF][START_REF] Seyfried | The Fundamental Diagram of Pedestrian Movement Revisited[END_REF][START_REF] Yanagisawa | Improvement of pedestrian flow by slow rhythm[END_REF][START_REF] Cao | Pedestrian dynamics in single-file movement of crowd with different age compositions[END_REF], we were interested in finding out how the pedestrians adapt if they are given more freedom.

For that purpose, we let the pedestrians choose their trajectories and -as a direct consequencedetermine the density collectively. To do so, we asked a fixed number of pedestrians (18) to walk along a circle, without further specification: Neither a center nor a radius were prescribed. Thus, a decision had to be made about the formation of the circle, which resulted both from a following behavior (interaction with the predecessor) and from a more global perception of the collective trajectory (see Fig. 1).

An intermediate case was also considered, in which pedestrians had to walk along a straight line across the sport facility. In this case, the path was fixed and the leader was imposing a maximal velocity, either his free velocity or a prescribed low velocity. Meanwhile, followers were free to choose their headways, or, in other words, the local density. Table 1 provides a summary of the realizations.

Fundamental diagram:

For each pedestrian, we define the instantaneous density as the inverse distance between the middle position of the pedestrian and its predecessor. In the case of a circular trajectory, the distance is the arc length. Instantaneous velocities are evaluated after filtering out the steps. To do so, we use a second-order low pass butterworth filter with a cut-off frequency of 0.8Hz. Computing these variables gives access to fundamental diagrams, an example of which is shown on Fig. 2 velocity, while on the other he was told to walk slowly. Recalling that followers are free to choose their headways, we notice that they chose it such that the resulting mean density-velocity point (black circle and diamond on Fig. 2-left) follows the fundamental diagram observed in similar experiments conducted at fixed density (Fig. 2-right) [START_REF] Jelic | Properties of pedestrians walking in line: Fundamental diagrams[END_REF]. The relation between velocity and density thus seems to be similar if one imposes the density or the velocity.

Fig. 2: Fundamental diagrams (right) for a circular path with density constraint (from [START_REF] Jelic | Properties of pedestrians walking in line: Fundamental diagrams[END_REF]) and (left) for two realizations of straight unidirectional flows, with a leader walking with free (green) or slow (blue) velocity; Small plus signs correspond to instantaneous (velocity, density) values, while thick symbols (circle and diamond) give the average values.

Response of dense crowds to local perturbations

We now turn to a study of static crowds at higher densities. In real life, these conditions are encountered in metro trains, at mass gatherings, or in front of a facility or a shop just before its opening (for instance, on Black Fridays in the US). Insight into the collective response of these crowds would be particularly valuable, because current agent-based models are generally not calibrated for these dense conditions and their predictions can therefore not be relied on.

Because of the density, pedestrian motion is strongly constrained sterically and physical contacts play a more and more important role in their interactions. It is appealing to handle the crowd as a dense physical medium and, effectively, research has pointed to quantitative similarities between the dynamics of dense crowds and granular media, for instance [START_REF] Helbing | Similarities between granular and traffic flow[END_REF][START_REF] Zuriguel | Clogging transition of many-particle systems flowing through bottlenecks[END_REF] . However, one should not forget that decisionmaking processes are also present and an exciting question is how the latter couple with the strong mechanical constraints.

Experimentally, the study of very dense crowds raises some challenges in terms of safety (in controlled experiments) and detection of tightly packed pedestrians. Overcoming these challenges, we performed controlled experiments to characterize the response of dense crowds of standing people to the crossing of an intruder, within the frame of Project PERCE-FOULE (collaboration between A. Nicolas at LPTMS and C. Appert-Rolland at LPT). The intruder will either be a real pedestrian making through the crowd or it will be abstracted into a moving cylindrical obstacle. Quite interestingly, these two experimental cases echo recent similar studies performed numerically on a minimalistic pedestrian model [START_REF] Metivet | How to push one's way through a dense crowd[END_REF] and experimentally on a granular medium penetrated by an intruder [START_REF] Kolb | Rigid intruder inside a two-dimensional dense granular flow: Drag force and cavity formation[END_REF][START_REF] Kolb | Flow fields around an intruder immersed in a 2D dense granular layer[END_REF], respectively. We aim to describe the local reorganization of the crowd triggered by these intrusions.

Description of the PERCE-FOULE experiments

After their formal approval by the local ethics committee (C3E), the experiments took place in in a sport facility at University Paris-Sud in Orsay (France) on 26 th , June 2017. They involved up to 39 voluntary participants, mostly students aged 20-30, with around 20% of women.

80-4

Proceedings of the 9 th International Conference on Pedestrian and Evacuation Dynamics (PED2018) Lund, Sweden -August 21-23, 2018 Paper No. 80 These participants were asked to stand in a delimited area (typically 4mx2.5m) and behave as if they were on an underground platform. They were wearing hats, with home-made bar codes (these are not used in the following), to facilitate the tracking. They were filmed from above by two TomTom Bandit cameras (60 frames per second, 1080p) and one Microsoft Kinect sensor (which provides the field of distances between objects and the focal plane of the sensor), hanging at an altitude of around 4 meters.

As already mentioned, two types of crossing experiments were performed, namely (i) pedestrian crossings, in which one participant was asked to walk to the opposite end of the crowd, (ii) crossing of a cylindrical obstacle. The role of the obstacle was played by one of the organizers, standing in a cylinder made of hula hoops of 74 cm in diameter and moving along a straight line. Type (ii) was expected to trigger larger deformations, with well-characterized obstacle shape and motion. Prior to each series of crossings, the crowd density was adjusted to an intermediate (~2 ped/m²), high (~4 ped/m²) or very high (~6 ped/m²) value by controlling the size of the standing zone while the pedestrians' orientation was prescribed to be either random, or facing the arrival of the obstacle. For each experimental condition, we performed 6 to 10 repetitions. Snapshots of one crossing by an obstacle are shown in Fig. 3.

Video analysis

30 images were extracted for every second of video footage (videos are thus downsampled) and corrected for the optical distortion of the lens (barrel distortion). We noticed that the cameras were rotating during the recording; this was corrected manually by applying rotations to each image so that given landmarks on the floor coincide between images.

We developed a home-made software in Python to detect and track the participants' hats on the basis of their colors. The algorithm proved very efficient and yielded almost no false negatives: virtually all hats were correctly tracked. Post-processing manual corrections allowed us to remove some spurious detections on the floor (false positives) and to track the obstacle.

The correspondence between the hat positions in pixel coordinates and the ground coordinates of the bodies was obtained by 1) finding the affine function that provides the best fit between the pixel coordinates of a subset of detected hats and the corresponding 'body' positions (defined as the middle of the feet, as determined manually when the person stands more or less straight) ; 2) converting pixel coordinates into ground coordinates via linear interpolation between reference points. The lens distortion (once corrected), the rotation of the cameras (once corrected) and the conversion between pixel coordinates and ground coordinates were found to create an experimental uncertainty of 80-5 only 5 cm or less. On the other hand, the correspondence between hats and 'bodies' (step 1 above) yielded an uncertainty of around 20 cm for not too inclined pedestrians, as we found by comparing estimated 'body' positions to manually measured positions on the videos [Fig. 4(left)]. This value is in line with our expectations, since we did not correct for the different participants' heights [START_REF] Boltes | Influences of Extraction Techniques on the Quality of Measured Quantities of Pedestrian Characteristics[END_REF], nor for the variations in the inclinations of their chests. Figure 4(right) corroborates this upper bound on the spatial inaccuracy by comparing trajectories that were reconstructed using videos from the first camera and from the second one. As a matter of fact, in this figure, the uncertainty is slightly lower than expected (less than 15 cm).

Preliminary results

In Fig. 5 we show the traces of the participants' motion in response to the crossing of the cylindrical obstacle, for an experiment at intermediate pedestrian density. The first conspicuous observation is that larger moves are made by people who stand close to the obstacle's route, which is quite intuitive. Less than two meters away from it, pedestrians barely move owing to the crossing, at this intermediate density. Furthermore, pedestrians do not appear to anticipate the passage of the obstacle much, as far as one can judge by the evolution of the trajectories with time.

Further analysis of these results will rely on averaging over nominally identical realizations and will be enlightened by comparison with (i) the displacements of grains in a two-dimensional packing due to a moving immersed intruder [START_REF] Kolb | Rigid intruder inside a two-dimensional dense granular flow: Drag force and cavity formation[END_REF][START_REF] Kolb | Flow fields around an intruder immersed in a 2D dense granular layer[END_REF], (ii) numerical simulations of passage of an individual through a crowd [START_REF] Metivet | How to push one's way through a dense crowd[END_REF]. In the granular setup, dramatic changes were observed as the packing fraction was increased towards the jamming point, with much larger force fluctuations and the disappearance of the cavity behind the intruder, through recirculation. Such cavity was also observed behind our cylindrical obstacle and was closed in a time scale of the order of the second after its passage at high enough density (compare the middle and right panels of Fig. 5). Besides, at a density just below the jamming density, the crosswise (x) profile of the average instantaneous streamwise (y) velocity of the grains obeyed the scaling

u y ( x ) ∼ ( x -x 0 ) e -( x-x 0 ) λ x
, with a lengthscale λ x ∼ 2 d (d is the grain diameter) that increases slightly with the size of the intruder. This seems compatible with our observations in dense pedestrian crowds, but it will be interesting to test whether the latter can also be described by the above formula.

80-6

Conclusion

In summary, we conducted experiments designed to shed light on the way pedestrians adapt their motion in order to cope with the constraints associated with walking or standing amid a group or a crowd. In particular, we presented results (i) on the pedestrians' adjustments of their headways in single-file motion where the leader's velocity is prescribed and (ii) on the response of a dense crowd to its crossing by a cylinder, drawing tentative parallels with the response of a two-dimensional granular packing.

We would like to conclude on a short note regarding the diverse methods for data collection presented here. VICON motion sensors provide temporally and spatially accurate localizations of the pedestrians' heads, but are a cumbersome and expensive system. Action cameras are cheaper and more portable, but are also slightly less accurate and do not directly measure the vertical coordinate (in our case leading to an experimental uncertainty on the positions close to 20cm, in part because we did not correct for the different participant's heights). Both methods require the participants to wear specific devices to facilitate their detection (although machine-learning algorithms may render this unnecessary). In contrast, depth-field sensors such as Microsoft Kinect cameras do not require pedestrians to wear specific markers or hats and are less invasive. On the downside, their field of view and spatial resolution are smaller than those of the other devices. Nevertheless, it is important to bear in mind that, besides the shortcomings of specific measurement devices, a major contributor to the uncertainty of the detected positions is inherent in the projection of the three-dimensional shapes of pedestrians onto (x,y)-positions. For instance, the position of the head with respect to the body is very sensitive to the (varying) inclination of the chest. In the future, to get a better grasp of the dynamics of dense crowds, which feature small spacings between pedestrians, it might become necessary to turn to a more suitable representation of the space actually occupied by the pedestrians' bodies.

Proceedings of the 9 th

 9 International Conference on Pedestrian and Evacuation Dynamics (PED2018) Lund, Sweden -August 21-23, 2018 Paper No. 80

Fig. 1 :

 1 Fig. 1: Snapshot taken during a unidirectional flow experiment, in which the participants walked along a circle that they were free to choose.

3

 3 -left for two realizations of straight walks. In one of them, the leader of the line walked at his free 80-Proceedings of the 9 th International Conference on Pedestrian and Evacuation Dynamics (PED2018) Lund, Sweden -August 21-23, 2018 Paper No. 80

Fig. 3 :

 3 Fig. 3: Snapshot of an experiment consisting in the crossing of a moderately dense crowd by a cylindrical obstacle. (Left) Image from the camera, in which the detected hats are highlighted and the tracked trajectories are shown. (Right) Image from the Kinect sensors. Light colors correspond to pixels that are closer to the focal plane of the camera (i.e., higher).

Fig. 4 :

 4 Fig. 4: (Left) Comparison between estimates of 'body' positions using the detected hat positions and actually measured positions. Data from different series of experiments are gathered here. (Right) Comparison between trajectories reconstructed using videos from the first camera (red) and the second one (black) in one crossing experiment.

  Fig. 5: Pedestrians' trajectories in the ground frame, in response to the crossing of a cylindrical obstacle, over the time windows indicated in the legends. The trajectory of the center of the cylinder is shown as a thick pink line and pedestrians were initially oriented in random directions.

Table 1 :

 1 Realizations of unidirectional pedestrian flows with unconstrained density.

	Trajectories	Number of repetitions Number of pedestrians
	Circle	6	18
	Straight with free velocity	7	36
	Straight with low velocity	3	36

Proceedings of the 9 th International Conference on Pedestrian and Evacuation Dynamics (PED2018) Lund,Sweden -August 21-23, 2018 Paper No. 80

Acknowledgements

We thank all participants in the experiments and, above all, the students and researchers who took an active part in their organization: Tom Marzin, Ioannis Touloupas, Aymeric Duigou-Majumdar, and Étienne Pinsard for the PERCE-FOULE experiments; Armel Cretual, Anthony Sorel, Dany Saligaut, Trenton Wirth, Gregory Dachner for the PEDINTERACT experiments. The PERCE-FOULE project was funded by a grant from French Labex PALM (ANR-11-IDEX-0003-02). 80-7 Proceedings of the 9 th International Conference on Pedestrian and Evacuation Dynamics (PED2018) Lund, Sweden -August 21-23, 2018 Paper No. 80

PEDINTERACT experiments were funded by the Inria SIMS associated team as well as the ANR PERCOLATION ANR-13-JS02-0008 project.