Ahmad Mortada

Sophie Carles

Sándor Demes

Baptiste Joalland

François Lique

Abdessamad Benidar

Panayotis Lavvas

Ludovic Biennier
email: ludovic.biennier@univ-rennes1.fr

Kinetics and Branching for the Reactions of N2+ with C3H4 Isomers at Low Temperatures and Implications for Titan's Atmosphere

Keywords: reactive collisions, uniform supersonic flows, temperature-dependent reactivity, planetary sciences, astrochemistry

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

I. INTRODUCTION

The Cassini-Huygens mission to Titan, which explored Saturn's largest moon from 2004 to 2017, has revealed a fascinating and complex world that could provide a good analogue of Earth during its early history. Under irradiation from UV solar photons, bombardment from galactic cosmic rays and high energetic electrons from Saturn's magnetosphere, the dense atmosphere of Titan, dominated by nitrogen N 2 and methane CH 4 , leads to the production of a wealth of organic species. Our knowledge of the atomic and molecular constituents of Titan's atmosphere, their spatial distribution and their temporal variations has also seen some significant progress through combined Earth-based and spacebased observations and in situ measurements. The composition of the dense troposphere has been determined by the Cassini Gas Chromatography/Mass Spectrometer (GCMS) measurements. [START_REF] Niemann | The Abundances of Constituents of Titan's Atmosphere from the GCMS Instrument on the Huygens Probe[END_REF] For the stratosphere, advances have relied on ground-based mm-wave instruments (IRAM, ALMA,…) [START_REF] Thelen | Abundance Measurements of Titan's Stratospheric HCN, HC 3 N, C 3 H 4 , and CH 3 CN from ALMA Observations[END_REF][START_REF] Marten | New Millimeter Heterodyne Observations of Titan: Vertical Distributions of Nitriles HCN, HC 3 N, CH 3 CN, and the Isotopic Ratio 15 N/ 14 N in Its Atmosphere[END_REF] , IR space observatories ISO [START_REF] Coustenis | Titan's Atmosphere from ISO Mid-Infrared Spectroscopy[END_REF] and Herschel [START_REF] Rengel | PACS Spectroscopy of Trace Gases of the Stratosphere of Titan[END_REF] , and the Composite Infrared Spectrometer (CIRS) embarked onboard Cassini [START_REF] Coustenis | The Composition of Titan's Stratosphere from Cassini/CIRS Mid-Infrared Spectra[END_REF] . The mesosphere has been characterized by the Cassini Visible Infrared Mapping Spectrometer (VIMS) [START_REF] Maltagliati | Titan's Atmosphere as Observed by Cassini/VIMS Solar Occultations: CH 4 , CO and Evidence for C 2 H 6 Absorption[END_REF] and Ultraviolet Imaging Spectrograph (UVIS) [START_REF] Koskinen | The Mesosphere and Lower Thermosphere of Titan Revealed by Cassini/UVIS Stellar Occultations[END_REF] . The much dilute high layer of the atmosphere, the thermosphere, has been investigated by the Ion Neutral Mass Spectrometer (INMS), which conducted mass spectrometric measurements of both ions and neutrals onboard Cassini. [START_REF] Waite | Ion Neutral Mass Spectrometer Results from the First Flyby of Titan[END_REF] In this particular region, a plethora of hydrocarbons (two-carbon acetylene C 2 H 2 , ethylene C 2 H 4 , and ethane C 2 H 6 , the three-carbon propyne/allene C 3 H 4 , propene C 3 H 6 and propane C 3 H 8 , the four-carbon diacetylene C 4 H 2 and the six-carbon benzene C 6 H 6 ) and nitriles (hydrogen cyanide HCN and hydrogen isocyanide HNC, cyanoacetylene HC 3 N, acetonitrile CH 3 CN, acrylonitrile CH 3 CCN, propanenitrile C 2 H 5 CN, cyanogen C 2 N 2 ) have been detected.

The INMS mass spectra spanning the 0-100 u range show peaks arranged in clusters separated by 10 to 15 u that coincide with the sequential addition of hydrogenated carbon or nitrogen atoms. Noteworthy, a good correspondence is found between the ion and neutral spectra. However, due to the low resolution of the embarked mass spectrometer (m/m~100), and the absence of isomer identification inherent to the method, the assignment of the peaks cannot be self-sufficient and relies heavily on a good knowledge of the chemistry. The latest modeling study based on INMS measurements [START_REF] Waite | Ion Neutral Mass Spectrometer Results from the First Flyby of Titan[END_REF] , and nitriles such as HCNH + . [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF] Many other ions stay under the radar because of mass overlap; they include N 2 + since HCNH + is the dominant species at m/z=28 u, and also N 2 H + concealed by C 2 H 5 + (m/z=29 u). To assess their presence, well-known reactions dominating their loss processes can be employed. The best tracer of N 2 + is considered to be CH 3 + as it can only be produced massively through the reaction of N 2 + with the second most abundant species in the atmosphere, methane CH 4 . [START_REF] Mcewan | Titan's Ion Chemistry: A Laboratory Perspective[END_REF][START_REF] Dutuit | Critical Review of N, N + , N 2 + , N ++ , and N 2 ++ Main Production Processes and Reactions of Relevance to Titan's Atmosphere[END_REF] The N 2 + cation is of particular importance as it is considered as a primary ion -i.e. generated in the early stages of the chemical network -along with N + and CH 4 + . These three cations are directly produced upon interaction of N 2 and CH 4 with solar photons and suprathermal photo-and secondary electrons.

Propyne CH 3 CCH has been first uncovered in the Voyager IR spectrum of Titan in the 80's. A stratospheric abundance of CH 3 CCH of 3×10 8 was determined for the mid-latitude region. [START_REF] Maguire | C 3 H 8 and C 3 H 4 in Titan's Atmosphere[END_REF] Further observations by ISO in 2003 led by Coustenis 4 provided a disk average value of 1.210 8 . During targeted flybys [START_REF] Magee | INMS-Derived Composition of Titan's Upper Atmosphere: Analysis Methods and Model Comparison[END_REF][START_REF] Cui | Analysis of Titan's Neutral Upper Atmosphere from Cassini Ion Neutral Mass Spectrometer Measurements[END_REF] , Cassini/INMS measured the abundance of propyne in the ionosphere and derived a mole fraction in the 2710 6 range. Propyne was also detected by the CIRS instrument [START_REF] Vinatier | Analysis of Cassini/CIRS Limb Spectra of Titan Acquired during the Nominal Mission: I. Hydrocarbons, Nitriles and CO 2 Vertical Mixing Ratio Profiles[END_REF] through its 633 cm -1 emission feature and through infrared observations made with the Texas Echelle Cross

Echelle Spectrograph (TEXES) on the NASA Infrared Telescope Facility. [START_REF] Lombardo | Detection of Propadiene on Titan[END_REF] Propadiene, also referred to as allene, CH 2 CCH 2 , an isomer of propyne, was unambiguously identified by TEXES observations through its emission near 12 m with a measured volume mixing ratio of 6.910 10 at the altitude of 175 km. CIRS measurements of propyne made at the same time indicate that the abundance ratio of propyne to propadiene is 8.2 at the same altitude. Propyne and propadiene constitute the first hydrocarbon isomer pair detected on Titan. Both isomers have been included in several photochemical models. [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF][START_REF] Li | Vertical Distribution of C 3 -Hydrocarbons in the Stratosphere of Titan[END_REF] According to Dobrijevic et al., [START_REF] Dobrijevic | 1D-Coupled Photochemical Model of Neutrals, Cations and Anions in the Atmosphere of Titan[END_REF] the main pathway for the formation of both isomers in the stratosphere is the associative reaction between hydrogen and propargyl radicals (C 3 H 3 ):

C 3 H 3 + H (+M)  C 3 H 4 (+M) (1)
Below 200 km, the CH 2 CCH 2 molecule can be produced additionally by the photodissociation of propene (C 3 H 6 ).

In the ionosphere, C 3 H 4 can be generated through the reaction of the CH radical with C 2 H 4 and through the recombination of C 3 H 5 + with electrons:

C 3 H 5 + + e  → C 3 H 4 + H (2)
The primary loss channel of C 3 H 4 is the photodissociation leading to propargyl C 3 H 3 :

C 3 H 4 + hѵ → C 3 H 3 + H (3)
Conversion from propadiene to propyne can take place through the reaction:

H + CH 2 CCH 2 → CH 3 CCH + H (4)
The ion and neutral chemistry proposed above is however incomplete as major sources of uncertainty remain, besides the fact mentioned above that the INMS measurements cannot alone rule out isomers and lead to a firm identification of the alleged species. In particular, major sources of uncertainty come from the lack of information on product identity and branching as well as their temperature dependence (available data are often restricted to room temperature). While this is especially problematic for radical-neutral reactions, with only one study below 50 K reported so far [START_REF] Abeysekera | Product Branching in the Low Temperature Reaction of CN with Propyne by Chirped-Pulse Microwave Spectroscopy in a Uniform Supersonic Flow[END_REF] , several techniques have been developed to measure the low-temperature kinetic rate coefficient and/or the products of ion-molecule reactions: crossed and merged molecular beams, ion traps and flow reactors.

Cryogenic ion traps are for instance tailored to examine the reaction kinetics of ions over a wide dynamic range. [START_REF] Gerlich | Ion-Neutral Collisions in a 22-Pole Trap at Very Low Energies[END_REF] In practice however, condensation of the neutral co-reactants onto the walls of the chamber limits their use to light neutrals such as H 2 or He. [START_REF] Wester | Radiofrequency Multipole Traps: Tools for Spectroscopy and Dynamics of Cold Molecular Ions[END_REF] Uniform supersonic flows, which belong to the family of flow reactors, are well adapted to explore quantitatively the reactivity of ions with large neutral molecules [START_REF] Biennier | Low Temperature Reaction Kinetics of CN -+HC 3 N and Implications for the Growth of Anions in Titan's Atmosphere[END_REF][START_REF] Bourgalais | Elusive Anion Growth in Titan's Atmosphere: Low Temperature Kinetics of the C₃N -+ HC₃N Reaction[END_REF][START_REF] Joalland | Low-Temperature Reactivity of C2n+1N-Anions with Polar Molecules[END_REF] it is one of the rare techniques to provide rate coefficients obtained under well-controlled thermalized conditions and over a wide range of low temperatures [START_REF] Biennier | Ion Chemistry in Uniform Supersonic Flows[END_REF] . Here, a new approach combining a CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme)

reactor with a mass-selective ion source [START_REF] Joalland | A Mass-Selective Ion Transfer Line Coupled with a Uniform Supersonic Flow for Studying Ion-Molecule Reactions at Low Temperatures[END_REF]

II. EXPERIMENTAL METHODS

The low-temperature reactions of N 2 + with C 3 H 4 isomers were investigated using a novel mass selective ion source (SIS) combined with a CRESU flow reactor. The experimental setup allows for measuring the absolute rate coefficient and the branching ratios of targeted gas-phase reactions at various low temperatures (down to 15 K). Details on this new approach can be found in previous work [START_REF] Joalland | A Mass-Selective Ion Transfer Line Coupled with a Uniform Supersonic Flow for Studying Ion-Molecule Reactions at Low Temperatures[END_REF] and are only briefly summarized hereafter. The neutral cold and dense uniform supersonic flow is generated by the isentropic expansion of a continuous buffer gas (here helium or a mixture of helium and nitrogen) through a de Laval nozzle. The density, velocity and temperature in the core of the supersonic flow are uniform over several tens of centimetres (See Table 1 for the characteristics of the de Laval nozzles used in this work). The buffer gas flow can reach 100 slm (standard liter per minute) thus requiring substantial pumping capacity (up to 35 000 m 3 /h) to maintain a low pressure (typically 0.1 mbar) in the main chamber. The high density of the flow (about 10 16 molecule cm -3 ) ensures local thermodynamic equilibrium and rapid rotational relaxation of the molecular species (charged or neutral). The supersonic flow, which can be viewed as a wall-less chemical reactor, was inseminated with a small quantity of the studied ionic and neutral reactants allowing reactive collisions. The neutral reactants propyne and allene (Air Liquide, 96% and 98% purity, respectively)

were injected continuously in the supersonic flow with a flow rate of a few sccm (standard cubic centimeter per minute) corresponding to a density of about 10 12 molecule cm -3 .

N 2 + ions were produced in a plasma generated by a hollow cathode discharge (P ∼ 2 mbar, U discharge  395 V, I discharge  950 mA) obtained with a continuous flow of helium (0.750 slm) and nitrogen N 2 (5 sccm). The mass selection of the N 2 + ions was performed by a quadrupole mass filter giving an output ion current of about 1 nA. Several quadrupole and octopole ion guides are used to transport ions from their production zone, through the selection mass filter and finally down to the uniform supersonic flow with a good transmission. The ion current measured at the injection lens of the SIS was about 600 pA. In this configuration, the ions arrive at right angle compared to the neutral uniform supersonic flow axis requiring a deflector with adapted applied potentials (around +3 V and -30 V for radial and vertical axes) to inflect their trajectory. According to Kato et al. [START_REF] Kato | Multiquantum Vibrational Deactivation of N 2 + (v) by Collisions with N 2 and O 2 at Thermal Energies[END_REF] and Ferguson [START_REF] Ferguson | Vibrational Quenching of Small Molecular Ions in Neutral Collisions[END_REF] , the collisional vibrational relaxation coefficient of N 2 + (v =1) by N 2 is about 5-8×10 -10 cm 3 molecule -1 s -1 , meaning that the relaxation to the ground state is achieved in a few µs, i.e. directly in the plasma of the SIS start station. As a result, the N 2 + ions are in their ground vibrational state before being injected into the uniform supersonic flow. The ionic species (reactants and products) were detected along the uniform supersonic flow axis by a moveable detector equipped with an entrance skimmer (80 µm diameter), a hexapole ion guide, a quadrupole mass filter (0-100 u), and a Channeltron ion multiplier. Because of the constant flow velocity, the moveable detector allows to follow the temporal evolution of the ion densities for a hydrodynamic time  h of typically 150-200 µs. for propyne and allene, respectively. [START_REF] Wilson | Reactions of Small Hydrocarbons with H 3 O + , O 2 + and NO + Ions[END_REF][START_REF] Milligan | Dissociative Proton Transfer Reactions of H 3 + , N 2 H + , and H 3 O + with Acyclic, Cyclic, and Aromatic Hydrocarbons and Nitrogen Compounds, and Astrochemical Implications[END_REF] ii. The H vi. For the C 3 H + product, all the reaction enthalpies calculated in this work for the different exit channels of the N 2 + + C 3 H 4 reactions are positive (see Figure 2), suggesting that the observed C 3 H + traces come from a secondary reaction between C 3 H 4 and some impurities. These reactions do not affect the evolution of the N 2 + density and therefore the derived rate coefficient of the studied reactions.

In order to qualitatively analyze the stoichiometry of the species observed in the mass spectra we performed a reduced theoretical analysis by calculating the enthalpies of formation and the corresponding relative reaction enthalpies by means of high level ab initio theories. The ab initio calculations were performed using the spin unrestricted coupled-cluster theory with single and double excitations (UCCSD) along with the augmented correlation-consistent valence double zeta (aug-cc-pVDZ) basis set. All calculations were carried out with the MOLPRO (version 2015.1) quantum chemistry software package [START_REF] Werner | Version 2015.1, a Package of Ab Initio Programs[END_REF][START_REF] Werner | [END_REF] . The structure and energy properties of all molecular species were determined in their minimum configuration, i.e. following full geometry optimization. Various starting geometries were examined in order to find the structures and properties of the most stable [N 2 -C 3 H 4 ] + complexes. Harmonic vibrational frequency and normal mode calculations were performed to compute the zero-point vibrational energies (ZPVE) and the total enthalpies of formation. More details about the geometries and energies of the species are given in the Supplementary Material. Given the low temperatures of the experiments, the N Accepted Manuscript / Final version Chesnavich and the Langevin models, respectively (see Figure 4), including between 24.1 K and 36.1 K where the total density is changed by more than 3-fold (18.310 [START_REF] Vinatier | Analysis of Cassini/CIRS Limb Spectra of Titan Acquired during the Nominal Mission: I. Hydrocarbons, Nitriles and CO 2 Vertical Mixing Ratio Profiles[END_REF] and 5.2810 16 molecule cm -3 , respectively). This set of observations strongly supports a bimolecular process only. pointed out in a work on the photoabsorption and photoionization of propyne [START_REF] Ho | Photoabsorption and Photoionization of Propyne[END_REF] . The examination of unimolecular decomposition process which has guided part of our analysis so far may provide some further hints. In the absence of quantitative determination of branching ratios between isomers from photoionization, one can turn to electron-impact ionization studies. Infrared spectroscopic measurements conducted by Brünken et al. [START_REF] Marimuthu | Laboratory Gas-Phase Vibrational Spectra of [C 3 H 3 ] + Isomers and Isotopologues by IRPD Spectroscopy[END_REF] showed that electron-impact ionization of allene CH 2 CCH 2 leads to the dominant production of the cyclic C 3 H 3 + isomer (81%) over the linear one (19%) and that the isomeric ratio is independent of the electron energy over the 14-70 eV range. Only a fraction of the energy of the colliding electron will effectively contribute to ionize and excite the molecule as most of it will be carried away with the electron itself after the encounter, since elastic electron scattering cross sections are typically orders of magnitude higher compared to the inelastic ones at such energies (see, e.g. Ref. [START_REF] Możejko | Absolute Total Cross-Section Measurements for Electron Collisions with Tetrahydrofuran[END_REF] ). The ionization process will take away the amount of energy corresponding to the adiabatic ionization potential of the target, allene, which is 9.7 eV and the remaining excess energy will be deposited as internal energy for the cations. Considering the electron energy range covered, one could expect that typically only a few of eV (see subsection 2.4 in Ref. [START_REF] Gross | Principles of Ionization and Ion Dissociation[END_REF] ) ends up in internal energy of the molecular target. Then, although direct photoionization and electronimpact ionization differ, one can expect a similar trend, supporting the hypothesis of a cyclic product to dominate. According to the energy diagram, this should also hold in the case of propyne.

Branching ratios

The formation of less prominent C 3 H 2 + is thought to occur directly from the CH 3 CCH + structure-note that we observed slightly more C 3 H 2 + with propyne than with allene. The cyclic isomer of C 3 H 2 + is also accessible, possibly without a barrier, but both these channels are not expected to contribute significantly.

The temperature dependence of the branching ratios gives further insights into these two competing CT mechanisms. While it has been shown previously that the near-resonant dissociative CT is largely independent of collision energy, [START_REF] Masson | Collision Mechanism of a Dissociative Charge-Transfer Reaction at Low Energy[END_REF] the nondissociative CT mechanism is not. Here, the slight but consistent increase of the yield toward C 3 H 4 + with decreasing temperature, associated with nonresonant, nondissociative CT for both target hydrocarbons, simply reflects the greater probability to form a bound complex at low collision energy, even after the long-range CT deposited such internal energy into C 3 H 4 + . Since the electron transfer processes are mainly driven by nonadiabatic couplings at long range, a quantitative explanation for this mechanism cannot be provided as the treatment of such complex processes is out of the scope of the present work. However, we can expect that, at lower collision energies, the charge transfer mechanisms lead to C 3 H 4 + cations with less internal energy and higher kinetic energy, which can be observed in the mass spectra as well. At higher temperatures, the primary C 3 H 4 + cation is formed with more internal energy which may effectively initiate a unimolecular decomposition into smaller species. Respectively, higher branching ratios are expected for the C 3 H 3 + and C 3 H 2 + products with less amount of C 3 H 4 + in this case.

C 3 H 3 + in Titan's atmosphere Latest models coupling ion and neutral chemical networks [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF][START_REF] Dobrijevic | 1D-Coupled Photochemical Model of Neutrals, Cations and Anions in the Atmosphere of Titan[END_REF] , supported by Cassini observations, have simulated the vertical density profile of many ionized and neutral organics in Titan's atmosphere. In terms of mole fraction, ionized species concentrate in the ionosphere spanning the 700-1400 km altitude range, where ionic processes play a key part in the chemistry [START_REF] Dobrijevic | 1D-Coupled Photochemical Model of Neutrals, Cations and Anions in the Atmosphere of Titan[END_REF] and in the formation of heavy molecules acting as aerosol embryos [START_REF] Lavvas | Aerosol Growth in Titan's Ionosphere[END_REF] . The generative or destructive role of ions is however not restricted to charged species and can notably include the production of neutrals, in particular through dissociative recombination. At an altitude of 1000 km, the most abundant hydrocarbons ions are C 2 H 5 + , C 3 H 3 + , C 3 H 5 + followed by CH 5 + , C 5 H 5 + and C 5 H 7 + 53 .

Among them, the C 3 H 3 + ion possesses two isomers, which cannot be observationally distinguished: the most energetically stable aromatic cyclopropenyl cation c-C 3 H 3 + and the linear propargyl cation l-

C 3 H 3 + .
The major loss process of ionic aromatic species in Titan's atmosphere is commonly considered to be dissociative recombination. Recent photochemical models [START_REF] Mcewan | Titan's Ion Chemistry: A Laboratory Perspective[END_REF][START_REF] Marimuthu | Laboratory Gas-Phase Vibrational Spectra of [C 3 H 3 ] + Isomers and Isotopologues by IRPD Spectroscopy[END_REF] confirm that (neutral) benzene is mainly generated in the thermosphere by ion chemistry and Loison et al. note that the large abundance of C 6 H 6 in the upper atmosphere is not the result of efficient formation pathways, but instead is due to the fact that once generated, the aromatic ring is preserved from photodissociation in the upper atmosphere. [START_REF] Dobrijevic | 1D-Coupled Photochemical Model of Neutrals, Cations and Anions in the Atmosphere of Titan[END_REF] The major loss process for c-C 3 H 3 + in Titan's atmosphere was also formally

Chemical reactivity of C 3 H 3 +

The reactivity of the C 3 H 3 + cation was investigated in the mid-90's in the laboratory at room temperature by employing a low pressure ICR trap (10 -6 mbar) [START_REF] Mcewan | Reactions of Isomeric C 3 H 3 + Ions: A Combined Low Pressure-High Pressure Study[END_REF][START_REF] Smyth | The Ion-Molecule Chemistry of C 3 H 3 + and the Implications for Soot Formation[END_REF] and highpressure SIFT methods ( mbar) [START_REF] Mcewan | Reactions of Isomeric C 3 H 3 + Ions: A Combined Low Pressure-High Pressure Study[END_REF][START_REF] Prodnuk | Gas-Phase Reactions of C 3 H n + Ions[END_REF][START_REF] Smith | Cyclic and Linear Isomers of C 3 H 2 + and C 3 H 3 + : The C 3 H + + H 2 Reaction[END_REF] . The linear isomer of C 3 H Accepted Manuscript / Final version

C 2 H 5 + + C 2 H 2  c-C 3 H 3 + + CH 4 (5) C 2 H 4 + + C 2 H 2  c-C 3 H 3 + + CH 3 (6) CH 3 + + C 2 H 2  c-C 3 H 3 + + H 2 (7)
with rate coefficients (in cm 3 molecule -1 s -1 units) of 6.84×10 -11 , 6.47×10 -10 for the reactions ( 5) and (6) in the Vuitton et al. [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF] .

N 2 + + C 3 H 4 : a new pathway to form c-C 3 H 3 + in Titan's ionosphere? Among all the detected hydrocarbon species, the two isomers of C 3 H 4 have been included in several photochemical models [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF][START_REF] Li | Vertical Distribution of C 3 -Hydrocarbons in the Stratosphere of Titan[END_REF][START_REF] Dobrijevic | 1D-Coupled Photochemical Model of Neutrals, Cations and Anions in the Atmosphere of Titan[END_REF][START_REF] Hébrard | Photochemistry of C 3 H p Hydrocarbons in Titan's Stratosphere Revisited[END_REF] . Their total abundance is comparable to C 2 H 2 and surpasses the one of the other considered C 3 hydrocarbons. In the coupled ion-neutral photochemical model of Vuitton et al. [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF] , the abundances of propyne CH 3 -C 2 H and allene CH 2 CCH 2 peak in the upper atmosphere with very similar calculated maximum mole fractions, e.g. of 1.5×10 -5 and 1.8×10 -5 cm -3 at 1075 km. Their combined contribution (3.3×10 -5 molecule cm -3 ) falls in between the uncorrected (6.310.24×10 -6 molecule cm -3 ) and corrected (1.40.9×10 -4 molecule cm -3 ) mole fractions from INMS [START_REF] Cui | Analysis of Titan's Neutral Upper Atmosphere from Cassini Ion Neutral Mass Spectrometer Measurements[END_REF][START_REF] Waite | The Process of Tholin Formation in Titan's Upper Atmosphere[END_REF] . Around the same altitude, from both Dobrijevic et al. [START_REF] Dobrijevic | 1D-Coupled Photochemical Model of Neutrals, Cations and Anions in the Atmosphere of Titan[END_REF] and Vuitton et al. [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF] photochemical models, the N 2 + abundance peaks at around 50 cm -3 (around 1100 km) for the first model and at 37 cm -3 (1125 km) for the second one which is the same order of magnitude as the CH exit channels, their inclusion in the chemical network will affect only marginally the overall chemical setting. The story is not the same for the cyclopropenyl c-C 3 H 3 + cation. Its reaction enthalpy is lower than that of l-C 3 H 3 + by 1.19 eV, and these isomers are protected from isomerization with a significant barrier of at least 2.17 eV. [START_REF] Marimuthu | Laboratory Gas-Phase Vibrational Spectra of [C 3 H 3 ] + Isomers and Isotopologues by IRPD Spectroscopy[END_REF] In a warmer environment, such as the one characterizing Titan's atmosphere above 800 km in which the gas temperature reaches 150 K, we can reasonably assume that the branching ratio into the c-C 3 H 3 + channel will be similar. Since the exoergicity is large, the additional energy corresponding to a temperature rise from 70 to 150 K should not allow populating much more levels. The branching ratio into C 3 H 3 + measured at 70 K of 0.85 can be then considered as a lower limit. Based on these premises and on the reported channel-specific reaction rate (see above) the reaction of N 2 + with C 3 H 4 isomers may participate in the production of c-C 3 H 3 + .

To evaluate the possible contribution of this pathway to the formation of c-C 3 H 3 + we included the evaluated reaction rates within a photochemical model of Titan's atmosphere [START_REF] Lavvas | Coupling Photochemistry with Haze Formation in Titan's Atmosphere, Part I: Model Description[END_REF] that has been updated with the latest chemical network coupling ion and neutral chemistry from Vuitton et al. [START_REF] Vuitton | Simulating the Density of Organic Species in the Atmosphere of Titan with a Coupled Ion-Neutral Photochemical Model[END_REF] lower than the total production rate (solid black line), while its column integrated contribution is about 2% of the total column production above 600 km.

V. CONCLUSION

The rate coefficients and the branching ratios for the reactions of N identified, the main one being C 3 H 3 + . The temperature-dependence of the branching ratios between these three exit channels show a subtle evolution toward more nondissociative charge transfer as the temperature decreases, a trend consistent with the formation of a bound complex occurring after the long-range charge transfer.

Our results, combined with previous work on the unimolecular decomposition of C 3 H 4 + , show that the reaction of N 2 + with both isomers of C 3 H 4 generates primarily C 3 H 3 + , plausibly under its cyclic form.

The lower reactivity of c-C 3 H 3 + with linear hydrocarbons compared to its linear l-C 3 H 3 + form [START_REF] Ausloos | Discrimination of C 3 H 3 + Structures on the Basis of Chemical Reactivity[END_REF] makes the presence of the cyclic isomer likely in Titan's atmosphere. Our evaluation on Titan's atmospheric photochemistry suggests that the contribution of this pathway to the formation of cyclic C 3 H 3 + is however of secondary importance relative to other pathways.

This work confirms the potential of our updated experimental approach in providing temperaturedependent branching ratios of ion-molecule reactions. Future experiments will focus on the reactivity of key molecular ions for astrophysical environments such as CH 3 + , whose neutral counterparts are not available off the shelf. Although reaction rates and branching ratios are available for a large selection of ion-molecule reactions, mostly at room temperature, large discrepancies between reported values persist and temperature dependence studies remain rare, especially at low temperatures.

H 4 +FIG 1 : 4 10

 414 FIG 1: Mass spectra measured in a 49 K uniform supersonic flow inseminated by mass-selected N 2 + cations in presence of CH 3 CCH (A) and CH 2 CCH 2 (B) neutral reactants at a density of 1.4

Figure 2

 2 Figure2shows the schematic diagram of the relative reaction enthalpies for the observed hydrocarbon

FIG 3: N 2 +

 2 FIG 3: N 2 + ion signal as a function of time for a range of neutral CH 2 CCH 2 densities (left) and corresponding loss rates as a function of CH 2 CCH 2 densities (right) at 24 K.

FIG 4 :

 4 FIG 4: Comparison between the measured absolute rate coefficients k as a function of temperature for the N 2 + with CH 3 CCH (red filled circles) and CH 2 CCH 2 (blue filled circles) reactions and the Langevin (blue dashed line) and Su & Chesnavich (red dashed line) models.

H 4 +

 4 , corrected to eliminate the contributions of the O 2 + + C 3 H 4 reactions, are shown in Figure 5 as a function of [C 3 H 4 ] density in the case of propyne at 49 K. The values vary slightly and linearly with the [C 3 H 4 ] density, due to secondary reactions of the primary ion products with C 3 H 4 . To limit the contribution of those reactions, the BRs were determined at short reaction times and by extrapolating their values for a null [C 3 H 4 ] density = 0 (y-intercept of the linear fit).

FIG 5 :FIG 6 :

 56 FIG 5: Evolution of the branching ratios (BRs) with the [CH 3 CCH] density, measured at 49 K for a reaction time of 56 μs. The BRs are corrected to eliminate the contribution of the O 2 + + C 3 H 4 reaction.

  identified as dissociative recombination, leading to the formation of c-C 3 H 2 or c-C 3 H 10 . In the work of McEwan et al.[START_REF] Mcewan | Reactions of Isomeric C 3 H 3 + Ions: A Combined Low Pressure-High Pressure Study[END_REF] , the authors pointed to the probable presence c-C 3 H 2 and encouraged its search. Two years ago, the smallest cyclic hydrocarbon cyclopropenylidene c-C 3 H 2 was effectively discovered in Titan by Nixon et al. with the help of the Atacama Large Millimeter/sub-millimeter Array (ALMA) radiotelescope, hence confirming this prediction.[START_REF] Nixon | Detection of Cyclopropenylidene on Titan with ALMA[END_REF]

FIG 8 :

 8 FIG 8: Contribution of different chemical pathways to the production of c-C 3 H 3 + in Titan's upper atmosphere. The indicated values represent the percentage contributions of each reaction to the total

TABLE 1 :

 1 Characteristics of the supersonic uniform flows employed in this study and determined from impact pressure measurements.

	Nozzle	Buffer gas	T jet (K) Mach	 (µs) n (10 16 molecule . cm -3 )	P chamber (mbar)	flow rate (l/min)
	He6K	He	24.1	5.84	196	18.3		0.630	93.4
	He36K	He	36.1	4.63	195	5.28		0.293	84.7
	Ar7K	He	49.0	3.87	150	10.4		0.770	67.0
	Ar7K	He/N 2 (1:1) 57.0	4.08	158	6.91		0.550	20:20
	Ar50K0.3 He	71.6	3.08	163	6.01		0.640	97.7
	III. RESULTS
	Reaction Products Figure 1 shows two mass spectra recorded at 49 K after a reaction time of t = 50
	µs and with a reactant density [C 3 H 4 ] = 1.4×10 12 molecule cm -3 for propyne and allene. For both
	reactions, the main ion product detected is C 3 H 3 + , followed by C 3 H 2	+ and C 3

  . The NO + + C 3 H 4 (propyne and allene) reactions have also been studied in SIFT experiments[START_REF] Wilson | Reactions of Small Hydrocarbons with H 3 O + , O 2 + and NO + Ions[END_REF] at 298 K. Propyne only generates the [C 3 H 4 NO] + adduct with a rate coefficient of k = 6.3×10 -11 cm 3 the NO + signal at low temperatures (a few percent) and the absence of an ion signal at m/z=70 u allow to discard any interference from the NO + + C 3 H 4 reactions. v. Two SIFT experiments have been performed at room temperature to examine the O 2 + + C 3 H 4 (propyne and allene) reactions. Wilson et al. only observed the charge transfer reaction, i.e. C 3 H 4 + + O 2 , with rate coefficients of k = 1.6 and 1.3×10 -9 cm 3 molecule -1 s -1 for propyne and allene respectively 30 . Dicker et al., also studied the O 2 + + CH 2 CCH 2 reaction and derived a rate coefficient k = 1.3×10 -9 cm 3 molecule -1 s -1 , but they observed three exit pathways: the charge transfer (94%), the C 3 H 3 + + HO 2 exit channel (4%) and the CH 2 CO + + CH 2 O one (2%) with calculated corresponding enthalpies ΔH = -2.39, -2.87 and -2.91 eV 34 . In the work of Wilson et al.

2 O + + C 3 H 4 reaction is considered as a source of C 3 H 5 + and potentially C 3 H 4 + in line with the proton affinities of propyne (748 kJ/mol) and allene (775.3 kJ/mol) which are larger than the ones of OH ( 593.2 kJ/mol) and H 2 O (691 kJ/mol). 32 The contribution of the H 2 O + + C 3 H 4 reaction to the BR of C 3 H 4 + is weak. As an illustration, the H 2 O + ion signal drops by less than 5 % in the presence of neutral reactant with a density [C 3 H 4 ] of 610 12 molecule cm -3 , meaning that H 2 O + is not highly reactive with C 3 H 4 . In spite of its small contribution, this effect is taken into account in the determination of the branching ratios of the N 2 + + C 3 H 4 reactions. iii. According to Milligan et al., N 2 H + reacts with C 3 H 4 to form the C 3 H 5 + ion exclusively as it has been observed in FA-SIFDT experiments at 300 K 31 . The experimental rate coefficients are k = 1.5 and 1.4×10 -9 cm 3 molecule -1 s -1 and the corresponding reaction enthalpies are ΔH = -2.87 and -2.91 eV for propyne and allene, respectively. ivmolecule -1 s -1 , while the reaction with allene exhibits two exit channels corresponding to the [C 3 H 4 NO] + adduct (90%) and the C 3 H 3 + ion (10%). However, the rate coefficient k = 2.5×10 -11 cm 3 molecule -1 s -1 for the NO + + CH 2 CCH 2 reaction is too low to be competitive here. The lack of a significant drop in 30 , the presence of vibrationally excited O 2 + ions was assumed. In the latter experiments of Decker et al. 34 , this issue was considered and O 2 was added to quench the excited O 2 + ions. This can explain the different results from the two SIFT experiments. Then, the C 3 H 4 + and C 3 H 3 + ions can also be formed by the O 2 + + C 3 H 4 reaction, this is considered in the branching ratio determination (see thereafter).

Table 2 .

 2 .22 eV, while the second isomer (pyrazole cation) has a slightly higher relative enthalpy, with about -6.20 eV. Both of these cations are highly exoergic with respect to the reactants and the C 3 H 4 + , C 3 H 3

	2 + + C 3 H 4 reactions can only form exoergic

+

cations remain out of reach. As one can also see in Figure

2

, the most exoergic N 2 C 3 H 4 + species have a cyclic structure. The first of them (1H-imidazole cation) has a very large relative exoergicity of about -Accepted Manuscript / Final version 7quasi-bound complexes (i.e. complex with large intramolecular distance, in agreement with the capture theory), producing excited C 3 H 4 + cations preliminarily. These complexes are represented by close superposition of the colliding molecular species, where their bond lengths and angles are not distorted, but where the electron exchange from C 3 H 4 towards N 2 + can effectively proceed, involving electronic transitions between multiple potential energy surfaces. This mechanism is supported by the Franck-Condon principle, according to which the electronic transitions proceed much faster than nuclear movements and rearrangements. If the primary cations are formed by conserving a large amount of internal energy, their dissociation proceeds according to a unimolecular decomposition scheme. Rate coefficients. Kinetic data were obtained under pseudo-first order conditions, i.e. with a [C

TABLE 2 :

 2 Absolute rate coefficients k of the N 2 + + CH 3 CCH and N 2 + + CH 2 CCH 2 reactions measured with the CRESU-SIS device at different temperatures in ×10 -9 cm 3 molecule -1 s -1 unit. The uncertainties take into account statistical and systematic (10%) contributions. CCH 2 , the rate coefficients show a quasi-independence with temperature. The measured values are in good agreement with the Langevin value of k L =1.38×10 -9 cm 3 molecule -1 s -1 estimated from k L =2𝜋𝑒√𝛼 𝜇 ⁄ , where e is the elementary charge, 𝛼 the static dipole polarizability of the neutral molecule (𝛼 𝐶𝐻2𝐶𝐶𝐻2 = 5.69 Å 3 from Ref.[START_REF] Gray | Fundamentals[END_REF] ), and 𝜇 the reduced mass of ion-molecule system. For N 2 + + CH 3 CCH, the Langevin model is not suitable since the permanent dipole moment µ D of the neutral reactant is not considered. For a polar neutral reactant, the Su and Chesnavich model[START_REF] Su | Parametrization of the Ion-Polar Molecule Collision Rate Constant by Trajectory Calculations[END_REF] gives a rate coefficient 𝑘 𝑆𝐶 = 𝐾 𝑐𝑎𝑝 × 𝑘 𝐿 which is temperature dependent with 𝐾 𝑐𝑎𝑝 = 0.4767𝑥 + 0.6200 when Considering the dipole moment of propyne (µ D =0.784 D)[START_REF] Rankin | CRC Handbook of Chemistry and Physics[END_REF] and its polarizability (𝛼 𝐶𝐻3𝐶𝐶𝐻 = 5.55 Å 3 )[START_REF] Gussoni | Electronic and Relaxation Contribution to Linear Molecular Polarizability. An Analysis of the Experimental Values[END_REF] , we determined for all the temperatures a value of the 𝑥 parameter greater than 2 for the studied N 2 + + CH 3 CCH reaction. Then the estimated values of the rate coefficients from the Su and Chesnavich model are 𝑘 𝑆𝐶 =3.49, 3.01, 2.70, and 2.38×10 -9 cm 3 molecule -1 s -1 at 24, 36, 49, and 71.6 K respectively. Figure 4, which displays the experimental values obtained in this work and the estimated values obtained from the simple capture models of Langevin and Su and Chesnavich, illustrates their remarkable agreement. Several arguments concur to rule out termolecular processes for the N 2 + + C 3 H 4 reactions. First, no peak at m/z= 68 u, corresponding to the association product, is detected in the mass spectra. Second, the rate coefficient of the N 2 + with CH 3 CCH reaction is not affected by changing the buffer gas, i.e. pure helium at 49.1 K and helium-nitrogen mixture (1:1) at 57 K. Thirdly, an increase of the total density or a decrease of the temperature both lead to a rise of the rate coefficient in a termolecular

	T (K)	24.1	36.1	49.1	57.0	71.6
	N 2 + + CH 3 CCH	3.73 ± 0.41	3.4 ± 0.36	2.52 ± 0.34	2.39 ± 0.25	2.13 ± 0.21
	N 2 + + CH 2 CCH 2	1.52 ±0.16		1.40 ±0.2		1.56 ±0.22
	For N 2 + + CH 2 𝑥 = µ𝐷 √2𝛼𝑇𝑘 𝐵 ≥ 2.

process; yet the measured rate coefficients for propyne and allene follow closely the Su and

  The C 3 H 2 + , C 3 H 3 + and C 3 H 4 + ions are clearly identified as the primary products of the N 2 + + CH 3 CCH / CH 2 CCH 2 reactions. The enthalpies of the N 2 + + C 3 H 4 reactions producing C 3 H + are positive and the formation of C 3 H 5 + is well explained by the reactions between N 2 + with impurities.

	As mentioned above as well, the O 2	+ + C 3 H 4 reaction represents however a small but non-negligible
	source (up to a few percent) of C 3 H 3 + and C 3 H 4 + ions, even if the initial abundance of N 2 + ions is much
	higher-by a factor of 16-than the abundance of O 2 + . In order to determine accurate branching ratios
	for the N 2 + + C 3 H 4 reactions, we have also explored the low-temperature reactivity of O 2	+ with
	propyne and allene with our CRESU-SIS experimental setup-the results will be presented in detail in
	an upcoming publication. In this case, the detected products are C 3 H 3 + , C 3 H 4 + , and C 2 H 2 O + (with
	branching ratios (T), (T), and (T), respectively), in agreement with Decker et al.'s observations for
	allene at 300 K. The small contributions of the O 2 + + C 3 H 4 reactions measured while studying the N 2 +
	+ CH 3 CCH / CH 2 CCH 2 reactions were eliminated by subtracting (T)O 2 + and (T)O 2 + to each of
	the C 3 H 3 + and C 3 H 4 + integrated peaks, respectively, with O 2 + representing the decrease of the O 2 + ion
	signal.
	The apparent BRs for the three exit channels C 3 H 2 + , C 3 H 3 + and C 3

TABLE 4 :

 4 Branching ratios of the reactions of N 2 + with the two C 3 H 4 isomers at 24.1, 36.1, 49.0 and 71.6 K. These values take into account the natural isotopic abundance of carbon 13.In the case of reactions of N 2 + with hydrocarbons, Gichuhi and Suits have measured the product branching for the reactions of N 2 + with methane CH 4 , acetylene C 2 H 2 , and ethylene C 2 H 4 at 40 K using a modified velocity map imaging apparatus.[START_REF] Gichuhi | Primary Branching Ratios for the Low-Temperature Reaction of State-Prepared N 2 + with CH 4 , C 2 H 2 , and C 2 H 4[END_REF] The reaction with acetylene was found to form onlyIn light of these previous results, the two CT mechanisms (dissociative and nondissociative) are likely responsible for the outcomes of the reactions studied here, although a careful mapping of the potential energy surfaces of the N 2 + + C 3 H 4 system would be necessary to fully validate this assumption. The measured rate coefficients, which are all collisional, indeed suggest that these fast reactions take place at long range via CT. The CT can deposit more than 5 eV of internal energy in the C 3 H 4

				CH 3 CCH			CH 2 CCH 2
	T (K)	24.1	36.1	49.0	71.6	24.1	36.1	49.0	71.6
	C 3 H 2 +	0.17	0.14	0.13	0.12	0.09	-	0.11	0.11
	C 3 H 3 +	0.72	0.77	0.83	0.85	0.785	-	0.83	0.85
	C 3 H 4 +	0.11	0.09	0.04	0.03	0.125	-	0.06	0.04
	IV. DISCUSSION
	only slightly more energetic than N 2 + (recombination energy of 15.76 eV for Ar + versus 15.58 eV for
	N 2 + ). The reported branching was 0.76:0.20:0.04 for C 2 H 2 + :C 2 H 3 + :C 2 H 4 + . The C 2 H 2 + :C 2 H 3 + ratio was
	found to increase further while increasing the internal energy of C 2 H 4	+ . From these measurements it
	was inferred that 95% of the CT excess energy is released into internal energy of the C 2 H 4 + ion before
	its decomposition. The authors concluded that the reaction proceeds via two competing mechanisms:
	i. A near-resonant, dissociative CT occurring at long range without significant momentum transfer.
	This mechanism is dominant and leads to the formation of C 2 H 2 + and C 2 H 3 + . It involves nonadiabatic
	transitions between charge states of N 2 + + C 2 H 4 and N 2 + C 2 H 4 + , which populate some of the C 2 H 4 +
	excited electronic states.
	ii. A nonresonant, nondissociative CT occurring via an "intimate collision" that enables significant
	momentum transfer. This mechanism is responsible for the C 2 H 4 + product, which is formed with less
	internal energy when compared to dissociative CT and therefore cannot decompose.

Reaction dynamics

To better understand the outcomes of the title reactions, we first invoke the reaction of Ar + with ethylene C 2 H 4 studied in a flowing-afterglow apparatus by Tsuji et al.

[START_REF] Tsuji | Dissociative Charge-transfer Reactions of Ar + with Simple Aliphatic Hydrocarbons at Thermal Energy[END_REF]

, as Ar + is Accepted Manuscript / Final version FIG 7: Potential energy diagram of the ground state of C 3 H 4 + , adapted from Mebel and Bandrauk 43 . Energies were calculated at the CCSD(T)/cc-pVTZ//B3LYP/6-311G ** level of theory and are shown relative to the global minimum, the allene cation CH 2 CCH 2 + . All the dissociation channels accessible for the ion precursor after charge transfer with N 2 + , which can deposit up to 5.89 eV into C 3 H 4 + , are reported. Note that no transition states were found for the H 2 loss channels from CH 2 CCH 2 + and c-C 3 H 4 + -dashed lines connect these stationary points.

excited states via CT might not necessarily dissociate following the lowest energy pathway, as e.g.

  3 + appears to be significantly more reactive with hydrocarbons than the cyclic isomer of C 3 H 3 + , due to a greater efficiency in forming a long-lived intermediate and also because the latter is more energetically stable. At high pressure or when the trapping time is long enough, this intermediate complex can be stabilized faster by collisions leading to larger rate coefficients such for the C 3 H 3 + + CD 4 , C 2 H 2 and C 2 H 4 reactions where the ionic adduct have been observed. For instance, the reactions between l-C 3 H 3 + and several small hydrocarbons of interest for Titan as C 2 H 2 , C 2 H 4 , C 3 H 4 (allene and propyne) and C 3 H 6 were measured with rate coefficients around 10 9 cm 3 molecule -1 s -1 in SIFT or ion trap experiments at room temperature, which is close to the Langevin rate constant. In summary, laboratory works evidenced the low chemical reactivity of the c-C 3 H 3 + ion, making it a terminal species of the chemical network.

	Formation pathways of C 3 H 3	+ in photochemical models The formation route of this carbocation is
	not completely secured. Recent photochemical models favor the ion -molecule reactions to form
	C 3 H 3 + because the radiative association of C 3 H + with H 2 to form C 3 H 3 + , a process which takes place in
	the interstellar cloud, presents a very low rate (below or around 10 -12 cm 3 molecule -1 s -1 ). These ion -
	molecule reactions mainly lead to the formation of the most stable cyclic c-C 3 H 3 + . In the work of Ali et
	al., a combination of calculations and experiments leads to the conclusion that under low temperature
	and pressure conditions of Titan's atmosphere, the hydrocarbon chemistry could play a fundamental
	role in the synthesis of organic compounds. The CH 3 + + C 2 H 2 or C 2 H 4 reactions generate the C 3 H 5 + ion
	which is followed by monomolecular decomposition yielding the cyclopropenyl cation c-C 3 H 3 + 60	. In
	others recent models, key ion -molecule reactions involve the three most abundant ions, C 2 H 5 + , C 2 H 4 +
	and CH 3 + with a density of above 10 cm -3 (420, 120 and 31 cm -3 respectively at 1125 km) and neutral
	acetylene C 2 H

2

, one of the most abundant hydrocarbons with a peak molar fraction around 3.1×10 -4 at 1077 km. These bimolecular reactions are:

  and Dobrijevic et al.[START_REF] Dobrijevic | 1D-Coupled Photochemical Model of Neutrals, Cations and Anions in the Atmosphere of Titan[END_REF] models and 2.88×10 -10 for the reaction(7) in the Vuitton et al. work and 1.15×10 -9 for the global reaction CH 3 + + C 2 H 2 in the Dobrijevic et al. study. Despite the same molar fraction as C 2 H 2 , ethylene C 2 H 4 (for which the INMS detection cannot be easily

	distinguished from that of C 2 H 2	15 ) is not considered as a possible source of c-C 3 H 3 + through the
	C 2 H 5 + , C 2 H 4 + , CH 3 + + C 2 H 4 reactions. Indeed, at the exception of an ICR study of the C 2 H 4 + + C 2 H 4
	reaction for which the C 3 H 3	+ product has been observed 61 , the numerous theoretical and experimental
	studies all conclude that the C 2 H 4	+ + C 2 H 4 and C 2 H 5 + + C 2 H 4 reactions do not form the C 3 H 3 + product
	62	. In contrast, C 2 H 4 can react with CH 3 + to preferentially produce the c-C 3 H 3 + isomer through the
	monomolecular decomposition of C 3 H 5 + but this reaction is not a preferred pathway due to its low rate
	coefficient (the experimental value obtained by ICR measurements is 9.2×10 -10 cm 3 molecule -1 s -1 ) and
	its branching ratio leading to the C 3 H 3 + formation (5%) 62 . At last, the fourth most abundant ion C 2 H 3 +
	with a density around 14 cm -3 at 1125 km 10 , reacting with C 2 H 2 or C 2 H 4 doesn't form C 3 H 3 + 62

  3 + density. The concentration of this primitive photolysis product cannot however be directly established by mass spectrometry because of the overlap with HCNH + considered to be 40 times more abundant and in a lesser extent with C 2 H 4 + .

	Our work combining laboratory experiments and theoretical considerations (see the energetic
	landscape of the Figure 7) shows that the reaction of N 2 + with both C 3 H 4 isomers generates dominantly
	c-C 3 H 3 + ions over the low temperature range explored (T= 2471.6 K) and to a lesser extent the C 3 H 2 +
	and C 3 H 4 + cations. The nature of the C 3 H 2	+ isomer remains elusive considering our incomplete
	understanding of the energetic landscape. However, given the low efficiency of the C 3 H 2 + and C 3 H 4 +

  . Our calculations suggest that the N 2 + + CH 3 C 2 H/CH 2 CCH 2 contribution has a secondary role compared to the dominant production terms from the reactions of C 2 H 4 + and C 2 H 5 + with acetylene (Figure 8). At the production peak near 1125 km, the cumulative contribution of the N 2 + + C 3 H 4 channels (dashed black line) is comparable to other secondary production pathways such as from reaction of CH 2 + with C 2 H 2 and CH 3 + with C 2 H 2 , C 2 H 4 and HC 3 N. However, at its maximum contribution the N 2 + pathway is ~40x

  2 + with propyne (CH 3 CCH) and allene (CH 2 CCH 2 ) have been experimentally determined at 24, 36, 49 and 72 K using the CRESU-SIS apparatus. All measured rate constants are collisional, agreeing remarkably with capture models. Three primary products C 3 H 2 + (m/z=38 u), C 3 H 3 + (m/z=39 u), and C 3 H 4

+ (m/z=40 u) have been clearly

ACKNOWLEDGMENTS

We express our gratitude to the referees for their time and valuable comments, which contributed to improve the quality of the manuscript. We thank J. Courbe for the mechanical design and J. Thiévin for the data acquisition. The implementation of the mass-selective ion source onto the CRESU reactor was funded by the Agence Nationale de la Recherche through the Anion CosChem Project (ANR-14-CE33-0013). We are grateful to Fasmatech for their expert help in ion optics. This work was also supported by the national research programs Physique et Chimie du Milieu Interstellaire (PCMI) and Programme National de Planétologie (PNP) of CNRS/INSU with INC/INP and cofunded by CEA and CNES. We wish to acknowledge the support from the CINES/GENCI for awarding us access to the OCCIGEN supercomputer within the A0070411036 project. Accepted Manuscript / Final version

SUPPORTING INFORMATION

The Supporting Information is available free of charge at https://pubs.acs.org/10.1021/acsearthspacechem.1c00347

It contains the calculated relative enthalpies for the product channels of the N 2 + + CH 3 CCH reaction at 0 K as well as the geometries, total electronic and zero-point vibrational energies and harmonic vibrational frequencies of all molecular species, which were studied by means of UCCSD/aug-cc-pVDZ theory.


Samir Audrey De Jong

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Better airway management saves lives


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Background calcium influx in arrhythmia: lead actor or extra?

Funsho Fakuade, J. Fauconnier, Niels Voigt

To cite this version:

Funsho Fakuade, J. Fauconnier, Niels Voigt. Background calcium influx in arrhythmia: lead actor or extra?. The Journal of Physiology, In press, 10.1113/JP283032. hal-03649832