Icarus 194 (2008) 746–757www.elsevier.com/locate/icarus

Low temperature (39–298 K) kinetics study of the reactions of the C4Hradical with various hydrocarbons observed in Titan’s atmosphere

Coralie Berteloite a, Sébastien D. Le Picard a,∗, Petre Birza a, Marie-Claire Gazeau b, André Canosa a,Yves Bénilan b, Ian R. Sims a

a Institut de Physique de Rennes, UMR UR1-CNRS 6251, Université de Rennes 1, Equipe “Astrochimie Expérimentale,” Bât. 11C,Campus de Beaulieu, F-35042 Rennes Cedex, France

b Universités Paris 12 et 7, Laboratoire Interuniversitaire des Systèmes Atmosphériques, UMR CNRS-Université No. 7583, Faculté des Sciences et Technologie,61 avenue du Général de Gaulle, 94010 Creteil Cedex, France

Received 3 August 2007; revised 8 October 2007

Available online 6 November 2007

Abstract

The reaction kinetics of the butadinyl radical, C4H, with various hydrocarbons detected in the atmosphere of Titan (methane, ethane, propane,acetylene, ethene and methylacetylene) are studied over the temperature range of 39–298 K using the Rennes CRESU (Cinétique de Réaction enEcoulement Supersonique Uniforme) apparatus. Kinetic measurements were made using the pulsed laser photolysis—laser induced fluorescencetechnique. The rate coefficients, except for the reaction with methane, all show a negative temperature dependence and can be fitted with thefollowing expressions over the temperature range of this study: kC2H6 = 0.29×10−10 exp(−25.6 K/T )× (T /298 K)−1.24 cm3 molecule−1 s−1;

kC3H8 = 1.06 × 10−10 exp(−56.3 K/T ) × (T /298)−1.35 cm3 molecule−1 s−1; kC2H2 = 1.82 × 10−10 exp(65.8 K/T ) × (T /298 K)−1.06 cm3

molecule−1 s−1, kC2H4 = 1.95 × 10−10 exp(−9.5 K/T )× (T /298 K)−0.40 cm3 molecule−1 s−1, kCH3C2H = 3.21 × 10−10 exp(−47.2 K/T )×(T /298 K)−0.82 cm3 molecule−1 s−1. These expressions are not intended to be physically meaningful but rather to provide an easy way tointroduce experimental results in photochemical models. They are only valid over the temperature range of the experiments. Possible channels ofthese reactions are discussed as well as possible consequences of these results for the production of large molecules and hazes in the atmosphereof Titan. These results should also be considered for the photochemistry of Giant Planets.© 2007 Elsevier Inc. All rights reserved.

Keywords: Titan; Atmospheres, chemistry; Organic chemistry; Atmospheres, composition

1. Introduction

Polyynes are unsubstituted acetylene-like linear compoundswith general formula C2nH2 [H–(C≡C)n–H]. To date, only thesimplest member of the series, C4H2 (H–C≡C–C≡C–H), di-acetylene, has been detected in the atmosphere of some plan-etary objects of our Solar System: Jupiter (Gladstone et al.,1996), Uranus (Burgdorf et al., 2006), Saturn (de Graauw et al.,1997) and its moon Titan (Kunde et al., 1981; Shemansky et al.,2005). Triacetylene (H–C≡C–C≡C–C≡C–H), C6H2, has been

* Corresponding author.E-mail address: sebastien.le-picard@univ-rennes1.fr (S.D. Le Picard).

0019-1035/$ – see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2007.10.012

identified in experimental simulations of Titan’s atmosphere(de Vanssay et al., 1995). Photochemically reactive in the UVrange, polyynes are thought to be one of the possible precursorsto the visible-absorbing haze materials present in many plane-tary environments (Allen et al., 1980). Such compounds mayplay, therefore, a key role in the chemistry of these planetaryatmospheres.

Indeed in photochemical models of Jupiter (Gladstone et al.,1996; Lebonnois, 2005; Moses and Greathouse, 2005), Saturn(Moses et al., 2000; Ollivier et al., 2000) and Titan (Wilson andAtreya, 2004, and references therein), polyynes are noteworthyfor their role in the formation of solid organic materials presentin the atmosphere of these objects. Current reaction networksmodeling the chemistry involved in the evolution of such envi-

Reaction kinetics of the C4H radical with various hydrocarbons in the atmosphere of Titan 747

ronments describe the formation via a polymerization processstarting from C2H2:

(C2)nH2 + hν → (C2)nH + H, (1)

(C2)nH + (C2)mH2 → (C2)(n+m)H2 + H. (2)

With the aim to refine the description of such mechanismsin models, polyynes have been the subject of various stud-ies. However, except for the simplest of them, acetylene C2H2,these compounds are not commercially available, and their syn-thesis and purification are more difficult to perform as thelength of the carbon chain increases. Furthermore, there is analmost complete lack of quantitative data relating to largerpolyynes due to their high thermal instability and their inclina-tion to polymerize at anything but the lowest partial pressures.

Nevertheless, absolute photoabsorption cross-sections ofsome of these species at relevant temperatures and over dif-ferent ranges of wavelength have been determined in order topredict the fate of those compounds under irradiation. Suchwork is essential for the modeling of radiative transfer andphotolysis rates. For example, for the two lightest polyynes,butadiyne (C4H2) and hexatriyne (C6H2), also called diacety-lene and triacetylene respectively, absorption cross-sectionshave been determined in the gas phase from 150 to 300nm and at relatively low temperature (Benilan et al., 1995;Fahr and Nayak, 1994; Okabe, 1981; Shindo et al., 2003;Smith et al., 1998).

The reaction kinetics of the building up of complex long-chain carbon compounds has also been studied. Most of theexperimental research however, has been undertaken in the con-text of combustion studies and, thus, has been conducted attemperatures of several thousands of degrees (Krestinin, 2000,and references therein). Only a very few rate coefficients havebeen measured under conditions relevant for astrophysical en-vironments, in particular at low temperatures (Smith, 2006).

Focusing on the case of Titan’s atmosphere, a complex pho-tochemistry that involves polyynes among other hydrocarbons,takes place over a temperature range of 70–175 K, N2 being thebackground gas. In such a medium, the formation of C4H2 isconfirmed by its detection in the stratosphere from the analy-sis of the infrared spectra recorded by the Voyager mission(Hanel et al., 1981; Kunde et al., 1981). Thus, to describe themechanisms involved, rate coefficients are required for reac-tions involving these species at low temperatures. Relativelyfew data are available, being limited to the reactions of theC2H radical with hydrocarbons with the work of Leone and co-workers employing laser photolysis and transient infrared ab-sorption spectroscopy in cooled cells down to 150 K (Hooblerand Leone, 1997, 1999; Opansky and Leone, 1996a, 1996b;Pedersen et al., 1993), the work of Sims, Smith and co-workersemploying laser-photolysis—chemiluminescence detection in aCRESU (Cinétique de Réaction en Ecoulement SupersoniqueUniforme or Reaction Kinetics in Uniform Supersonic Flow)apparatus (Carty et al., 2001; Chastaing et al., 1998), and thework of Leone and co-workers using the latter detection tech-nique in a pulsed CRESU apparatus (Goulay and Leone, 2006;Lee et al., 2000; Murphy et al., 2003; Nizamov and Leone,2004a, 2004b; Vakhtin et al., 2001a, 2001b).

Up to now, no data concerning the higher homologues wereavailable in the literature as they are very unstable compounds.In these circumstances, the only way for modelers to includethese reactions in their chemical schemes is to evaluate theirrate coefficients from similar reactions for which rates areavailable in the literature. Thus, arguing that higher polyyneradicals are probably less reactive than C2H, rate coefficientsfor (C2)nH + hydrocarbon reactions have been arbitrarily setto k((C2)nH) = 31−nk(C2H) by the authors of the first pho-tochemical models of Titan’s atmosphere (Lara et al., 1996;Toublanc et al., 1995; Yung et al., 1984). More recently, theassumption adopted by Wilson and Atreya (2004), Burgdorf etal. (2006), Hébrard et al. (2007) is that all (C2)nH reaction ratesare equal to their C2H analogues.

In spite of the use of the updated laboratory low temperaturedata, and thus the subsequent improvement of the descriptionof the chemistry of hydrocarbons, the mole fractions estimatedfrom the photochemical models do not well reproduce the ob-servations (Hébrard et al., 2007; Vinatier et al., 2007). Forexample, Table 1 shows that C4H2 is either overestimated orunderestimated compared to the concentration measured in Ti-tan’s atmosphere by ISO (Infrared Space Observatory) or CIRS(Composite InfraRed Spectrometer onboard the Cassini space-craft orbiting Saturn) experiments at a given range of altitude(respectively 75–260 and 98–187 km). Moreover, the theoret-ical data for diacetylene, even those that take into account theerror bars for the kinetic rate coefficients, do not fit the very lastprofile obtained from CIRS limb data (Vinatier et al., 2007).In fact, this is the case for the majority of unsaturated hydro-carbons detected in Titan’s stratosphere. Since mean concen-trations appear to be controlled essentially by chemical ratherthan physical parameters (Lebonnois et al., 2001), this discrep-ancy is probably due to a deficiency in the estimation of kineticparameters relating to the destruction or formation of C4H2(Hébrard et al., 2007).

Another feature of Titan’s atmosphere is the presence of dif-ferent layers of haze that give its orange-brown color whenobserved in the visible. The sources and mechanisms lead-ing to the formation of these hazes are still poorly under-stood. Photochemical formation of hazes has been exploredfor more than twenty years. Although laboratory simulationshave shown that formation of aerosol particles could involvephotolysis of acetylene (C2H2), ethylene (C2H4), and hydro-gen cyanide (HCN), the difficulty of performing simulationsof these processes under the conditions of the atmosphereof Titan makes those results quite speculative. The possibleroles of polyynes (Yung et al., 1984), nitriles (Banaszkiewicz,2000) and more recently aromatics (Lebonnois et al., 2002;Wilson and Atreya, 2003) have been studied in various models.The scarcity of kinetic measurements however, especially un-der the physical conditions of the atmosphere of Titan, makesthese analyses uncertain.

We suggest that reactions of the type (2) could play a rolein the formation of long polyacetylenic chains and large mole-cules. The kinetics study at low temperatures of C4H radicalreactions with various hydrocarbons among the most abun-dant observed in Titan’s atmosphere (CH4, C2H2, C2H4, C2H6,

748 C. Berteloite et al. / Icarus 194 (2008) 746–757

Table 1Comparison between mixing ratios observed by ISO (2003) and the Cassini CIRS instrument (2005) with various photochemical models

Compound Altitude(km)

Model Observation

Yung et al.(1984)

Toublanc et al.(1995)

Lara et al.(1996)

Lebonnois et al.(2001, 2002)

Wilson andAtreya (2004),nom. withfractal: Miehaze

ISOalt. 75–260 km,Coustenis et al.(2003)

CIRSalt. 98–187 km,10◦ S, Flasar etal. (2005)

C2H6 125 2.0 × 10−4 1.2 × 10−5 8.7 × 10−6a 2.7 × 10−6 5.8 × 10−6 2.0 ± 0.8 × 10−5 1.8+0.3−0.45 × 10−5

1.2 × 10−5

C2H2 125 4.3 × 10−5 2.2 × 10−6 3.0 × 10−6a 1.9 × 10−6 1.9 × 10−6 5.5 ± 0.5 × 10−6 3.0+0.1−0.2 × 10−6

1.1 × 10−6

C3H8 105 4.2 × 10−6 2.8 × 10−7 1.0 × 10−7b 2.4 × 10−7 6.3 × 10−8 2.0 ± 1.0 × 10−7 5.9+2.1−2 × 10−7

2.8 × 10−7

C2H4 125 3.1 × 10−7 3.2 × 10−9 8.3 × 10−8 2.1 × 10−8 9.4 × 10−9 1.2 ± 0.3 × 10−7 2.1+0.7−0.2 × 10−7

1.5 × 10−8

CH3C2H 105 9.5 × 10−7 1.4 × 10−8 2.3 × 10−11 9.8 × 10−10 1.8 × 10−9 1.2 ± 0.4 × 10−8 9.0+1−1.5 × 10−9

6.6 × 10−10

C4H2 105 1.6 × 10−10 6.8 × 10−9 4.7 × 10−9c 3.9 × 10−9 6.2 × 10−10 2.0 ± 0.5 × 10−9 1.3+0.3−0.2 × 10−9

1.9 × 10−9

a Mixing ratio at 130 km.b Mixing ratio at 125 km.c Mixing ratio at 110 km.

CH3C2H and C3H8) that we present here should help modelersto assess this assumption.

2. Experimental technique

The CRESU technique which is now well established for thestudy of gas phase reaction kinetics at very low temperatures(Dupeyrat et al., 1985; Sims et al., 1994), has been used in thepresent study. Here, we concentrate on those features of ourexperiments which are specific to kinetic experiments on thereactions of C4H radicals.

In the CRESU technique, low temperatures are achieved viathe isentropic expansion of a buffer gas through a Laval nozzle.Each nozzle employed provides an axially and radially uniformsupersonic flow at a particular temperature, density and velocityfor a given buffer gas. The relatively high density of the super-sonic flow (1016–1017 cm−3) ensures frequent collisions, thusmaintaining thermal equilibrium. All these properties are con-served in the core of the supersonic flow over a typical distanceof a few tens of centimeters along the flow corresponding to ahydrodynamic time of several hundreds of microseconds. TheLaval nozzle is mounted on a reservoir kept at room tempera-ture into which the buffer gas, the C4H precursor molecule andthe reagent gases were injected.

C4H radicals were created by the pulsed laser photolysis ofdiacetylene, C4H2, using the 248 nm radiation of a KrF excimerlaser (Lambda Physik, LPX 200). The beam from this laser en-tered the CRESU chamber through a Brewster angle windowand propagated counter to the gas flow.

C4H2 was synthesized by dehydrochlorination of 1,4-di-chloro-2-butyne (C4H4Cl2) (Khlifi et al., 1995). Given the highinstability of diacetylene, only small amounts were synthesizedbefore a series of kinetic experiments. Once synthesized, C4H2was mixed with helium gas in a 20 L glass vessel at a total

pressure of ca. 1.2 bar. He–C4H2 mixture was injected into thereservoir of the CRESU chamber using very small flows of theorder of a few standard cm3 min−1.

C4H radicals were detected by laser induced fluorescence(LIF) using a 2Σ

+–2Σ

+vibronic band type of the B2Πi–X2Σ

+

electronic system. Laser radiation at a wavelength of ca. 408 nmwas generated using the frequency doubled output of a Nd:YAGlaser (Continuum, Powerlite Precision II) to pump a dye laser(Laser Analytical Systems, LDL 20505) operating with Styryl9M dye (Sigma–Aldrich) in methanol, the output of which wasfrequency doubled in a BBO crystal. The linewidth of the UVlaser was measured with a wavemeter (HighFinesse/Angstrom,WS-7R) to be 0.24 cm−1. This probe laser entered the CRESUchamber and gas reservoir through two quartz Brewster an-gle windows and passed through the Laval nozzle throat anddown the gas flow along its axis counter to the direction ofthe photolysis beam. Fluorescence from C4H (B2Πi ) was col-lected at right angle to the laser propagation direction usingan optically fast collection system, and detected with a pho-tomultiplier tube (Thorn EMI, 9813 QSB) through a low-passglass filter (Schott, GG 435). The signal from the PMT wasrecorded by a gated integrator and a boxcar averager (StanfordResearch Systems) and transferred to a PC via an IEEE inter-face (Stanford Research Systems, SR 245) controlled by dataacquisition software. The time delay between the pump andprobe beams, which was scanned to generate decay traces, wascontrolled by a four-channel delay/pulse generator (StanfordResearch Systems, DG535), which was also controlled by thesame data acquisition software via an IEEE interface.

A typical LIF decay trace for C4H at 52.3 K is shown inFig. 1. As can be seen, a finite rise time was observed for theC4H LIF signal. This was taken as resulting from collisional re-laxation of C4H formed in electronic and/or rotationally excitedstates. Indeed, the first excited electronic state of C4H, A2Π , is

Reaction kinetics of the C4H radical with various hydrocarbons in the atmosphere of Titan 749

Fig. 1. Decay of C4H (2Σ+

–2Σ+

) LIF signal at 52.3 K in the pres-ence of C2H6 ([C2H6] = 0.43 × 1014 cm−3) and Ar buffer ([Ar] =10.3 × 1016 cm−3), fit to a single-exponential function.

predicted to lie very close to the ground state, with theoreti-cal estimations varying from 70 to 565 cm−1 (Sobolewski andAdamowicz, 1995; Woon, 1995). Photoelectron spectroscopyexperiments of C4H− anions allowed the authors to give anupper limit for the energy of the A2Π state: Neumark and co-workers (Taylor et al., 1998) gave an upper value of 468 cm−1,while more recent experiments by Pino et al. (2002) wereconsistent with an A2Π state lying at a lower energy of ca.160 cm−1 above the X2Σ

+ground state, which is a value cited

as a private communication by Endo and co-workers in the pa-per by Neumark and co-workers (Taylor et al., 1998). In order toavoid contamination of the data, all nonlinear least-squares fitsof the exponential decays of the LIF signals were started afterthis rise corresponding to electronic and/or rotational relaxationof C4H was complete, and pseudo-first-order decay times werekept at least ten times longer than this rise time. For a giventemperature, LIF scans were then taken for different reagentconcentrations in the usual way in order to construct a kineticplot from which the second-order rate coefficient could be ex-tracted. Fig. 2 shows a second-order plot for C4H + C2H6 at52.3 K. Measurements at room temperature were performedin the CRESU apparatus as previously described (Sims et al.,1994).

Hydrocarbon reagents were mixed with the buffer gas beforepassing into the reservoir and expanding through the Laval noz-zle. CH4 (99.995%), C2H4 (99.95%), C2H6 (99.995%), C3H4

(methyl acetylene) (96%) and C3H8 (99.95%), all from AirLiquide, C2H2 (99.6%, AGA) and carrier gas (N2 and Ar;Air Liquide, 99.995%) were taken directly from cylinders andregulated by means of calibrated MKS mass flow controllers.Knowledge of the total gas density along the flow, and of theindividual gas flow rates, allowed the hydrocarbon concentra-tions in the supersonic flow to be calculated.

Fig. 2. Second order plot for the reaction of C4H + C2H6 at 52.3 K inAr, leading to a value for the second-order rate coefficient of k = (1.81 ±0.02) × 10−10 cm3 molecule−1 s−1.

3. Results

3.1. C4H spectra

To our knowledge the most recent spectroscopic work onneutral C4H was published by Endo and co-workers (Hoshina etal., 1998; Pino et al., 2002). In their paper, Hoshina et al. (1998)present and analyze twenty vibronic bands of C4H observed bylaser induced fluorescence (LIF) in the 24000–25000 cm−1 re-gion, corresponding to the range of wavelengths 400 to 416 nm.Fig. 3 shows a survey spectrum obtained in our experimentat 52 K for a time delay between the photolysis laser and theprobe laser of 20 µs over the same wavelength range. Most ofthe vibronic bands observed by Endo and co-workers (Hoshinaet al., 1998) are also present in our spectrum, only the weak-est of them are absent. We did not, however, see any of the C3

features which were observed by Endo and co-workers prob-ably as a result of their use of a discharge source, in contrastto the more specific photolytic source of C4H radical used inthis study. We have performed a theoretical simulation of theentire band system using the spectroscopic parameters deter-mined by (Hoshina et al., 1998). Some bands also present inthe spectra of Endo and co-workers clearly show up here. Theycannot be attributed to C3 since it is not present in detectableamount in our spectra (less than 1% relative to C4H). A com-plete reanalysis of the C4H band system will be presented else-where. To perform our kinetic measurements we used the bandat 24,490.8 cm−1 referred to as the [J] band (correspondingto a transition from the ground state to the B2Πi3ν5(Σ

+) ex-cited state) by Endo and co-workers, as this band is one of themost intense and suffers least from overlap with other bands.Fig. 4 shows this band observed in our experiment at 52 K, aswell as a simulation calculated using the spectroscopic parame-ters determined by Hoshina et al. (1998) except for a rotationalconstant of the upper state B ′

eff = 0.1512(1) cm−1 and spinsplitting constant Γ ′ = 0.009(1) cm−1. The band is quite wellreproduced, apart from the perturbed lines as already noticedby Hoshina et al. (1998), with a Voigt profile using a resolutionof 0.08 cm−1.

750 C. Berteloite et al. / Icarus 194 (2008) 746–757

Fig. 3. LIF spectrum survey at 52.3 K of products of C4H2 photolysis at 248 nm. Simulation was calculated using a temperature of 50 K, a Voigt profile of 0.08 cm−1

(FWHM) and spectroscopic parameters derived by Hoshina et al. (1998). Transitions [A–W] belong to the C4H radical according Hoshina et al. (1998).

Fig. 4. LIF spectrum of a 2Σ+

–2Σ+

[J] band of C4H. Observed spectrum is obtained at 52.3 K, simulation was calculated using a temperature of 50 K and a Voigtprofile of 0.08 cm−1 (FWHM).

To obtain the kinetic measurements presented in the nextsection, we used the R-band head of the transition, which isthe most intense part of this spectrum, as can be seen in Fig. 4.

3.2. Kinetic measurements

Our experimentally measured rate coefficients are summa-rized in Table 2 which also reports the main flow conditionsfor each study. The quoted uncertainties comprise statistical er-rors calculated as the standard error obtained from the fit ofthe second-order kinetic plot multiplied by the appropriate Stu-dent’s t factor for the 95% confidence limit combined with anestimate of possible systematic errors. The latter are essentiallydue to flow control inaccuracies or inaccuracies in the determi-nation of the buffer gas total density. Every effort was made tominimize these and we estimate that they do not exceed 10%.

In Figs. 5–9, the rate coefficients k(T ) that we obtained aredisplayed as a function of the temperature on log–log plots. Re-sults of the fittings of the data are presented in Table 3, using theequation k(T ) = A exp(−θ/T )(T /298 K)n and the resultingvalues of A, θ and n are given. We emphasize that these ex-pressions are only valid over the temperature range 39–300 K.They are not intended to be physically meaningful but rather toprovide an easy way to introduce experimental results in photo-chemical models with a good level of confidence, as these fitsdo not generally deviate too much from our measurements.

In every case, with the exception of methane, the rate coef-ficients for the reactivity of hydrocarbons with C4H are closeto the collisional rates and show slight negative temperature de-pendences. In the case of methane, which reacts much moreslowly, we were not able to obtain any rate coefficient below200 K. The measurements are limited by both the length and

Reaction kinetics of the C4H radical with various hydrocarbons in the atmosphere of Titan 751

Table 2Rate coefficients measured at different temperatures for the reactions of C4H with CH4, C2H2, C2H4, C2H6, C3H8 and CH3C2H

Temperature (K) 39 52 83 145 200 298 298Carrier gas N2 Ar N2 N2 N2 Ar N2Total density 3.3 10.3 4.9 9.2 5.8 25 21.5(1016 molecule cm−3)

Range of reactant gas density (1012 molecule cm−3)CH4 350–3500 1 × 103–1 × 104

C2H2 3–32 13–77 2.5–47.5 10–110 13–264C2H4 3–33 14–137 4–26 10–110 25–386C2H6 13–134 10–107 19–192 89–448 215–1039C3H8 7–27 7–79 8–7 13–66 78–728CH3C2H 2–14 5–33 3–34 8–79 14–164

Rate coefficient (10−10 cm3 molecule−1 s−1)CH4 0.77 ± 0.12 × 10−2 2.13 ± 0.2 × 10−2

C2H2 2.57 ± 0.35a 3.88 ± 0.41 2.74 ± 0.28 2.54 ± 0.32 1.54 ± 0.16C2H4 5.57 ± 0.64 4.84 ± 0.49 3.19 ± 0.39 3.27 ± 0.35 1.80 ± 0.19C2H6 1.75 ± 0.18 1.81 ± 0.18 0.78 ± 0.09 0.58 ± 0.06 0.41 ± 0.04C3H8 3.70 ± 0.43 4.15 ± 0.42 2.72 ± 0.39 1.88 ± 0.26 1.03 ± 0.11CH3C2H 4.93 ± 0.58 5.66 ± 0.60 5.04 ± 0.62 4.13 ± 0.53 2.80 ± 0.38

a Uncertainties (here and throughout the tables) are calculated using standard error evaluated from the second order plot, multiplied by the Student’s t factor(95%). A systematic error of 10% was added to take into account contribution from possible systematic errors.

Fig. 5. Rate coefficients for the reaction of C4H with CH4 as a function of tem-perature, displayed on a log–log scale. The filled circles show the experimentalresults obtained in this work. The dashed lines represent equations used for thisreaction in various photochemical models of the atmosphere of Titan. The longdashed line represents data from Wilson and Atreya (2004), the medium dashedline from Toublanc et al. (1995), the dotted line from Lara et al. (1996) and thedash-dotted line from Yung et al. (1984).

therefore the duration of the supersonic flow, as well as themaximum concentration of hydrocarbon possible without ei-ther perturbing the supersonic flow, or causing condensation.These limitations preclude the determination of rate coefficientsslower than ∼5 × 10−13 cm3 molecule−1 s−1.

Most of the rates were obtained using nitrogen as a buffergas, with the exception of the measurements at 52 K and someof the measurements at 298 K that were obtained using ar-gon as a buffer gas. Considering the temperature dependencesk(T ), results derived in argon are fully consistent with thoseobtained in nitrogen, showing no effect of the nature of thebuffer gas (N2 or Ar) on the rate coefficients measured. In ad-dition, at 50 K we performed kinetic experiments for all gaseswith nozzles giving two different densities: 0.52 × 1017 cm−3

and 1.01 × 1017 cm−3. In both cases the rates obtained werethe same, within the uncertainty of our experiments. At 298 K,measurements with methane were also performed at two den-sities, 0.68 × 1017 and 2.07 × 1017 cm−3, respectively, and therate coefficients were found to be similar. These results indicatethat either all these reactions are bimolecular or that they wereobtained in the high pressure limit of a termolecular process,the third body being the buffer gas (N2 or Ar).

Table 3Fit parameters (A, θ , n) of our kinetic data according to the following equation k2nd = A exp(−θ

T)( T

298 K )n for each reagent C2H2, C2H4, C2H6, C3H8 andCH3C2H, in the range T = 39–300 K

A

(10−10 cm3 molecule−1 s−1)θ (K) n Estimated uncertaintya

(10−10cm3 molecule−1 s−1)

C2H2 1.82 65.8 −1.06 0.75C2H4 1.95 −9.5 −0.40 0.65C2H6 0.29 25.6 −1.24 0.37C3H8 1.06 56.3 −1.35 0.48CH3C2H 3.21 47.2 −0.82 0.29

a Corresponds to 2σ with σ =√ ∑

(k2nd exp−k2ndfit)2

number of experimental points .

752 C. Berteloite et al. / Icarus 194 (2008) 746–757

Fig. 6. Rate coefficients for the reaction of C4H with C2H6 as a function oftemperature, displayed on a log–log scale. The filled triangles down show theexperimental results obtained in this work and the bold solid line shows the fitto these data. The other dashed lines represent equations used for this reactionin various photochemical models of the atmosphere of Titan. The long dashedline represents data from Wilson and Atreya (2004), the medium dashed linefrom Toublanc et al. (1995), the dotted line from Lara et al. (1996) and thedash-dotted line from Yung et al. (1984).

Fig. 7. Rate coefficients for the reaction of C4H with respectively C3H8 andCH3C2H as a function of temperature, displayed on a log–log scale. The filledsquares show the experimental results obtained in this work for C3H8 and thebold solid line shows the fit to these data. The filled triangles show the experi-mental results obtained in this work for CH3C2H and the solid line shows thefit to these data.

4. Discussion

4.1. Temperature dependences and possible products of thereactions

In this subsection, we comment the temperature depen-dences observed in our experiments and give some insights onthe possible products formed by these reactions. More detailson the chemistry of these reactions, and others involving C4H

Fig. 8. Rate coefficients for the reaction of C4H with C2H2 as a function of tem-perature, displayed on a log–log scale. The filled circles show the experimentalresults obtained in this work and the bold solid line shows the fit to these data.The other dashed lines represent equations used for this reaction in various pho-tochemical models of the atmosphere of Titan. The long dashed line representsdata from Wilson and Atreya (2004), the medium dashed line from Toublanc etal. (1995), the dotted line from Lara et al. (1996) and the dash-dotted line fromLebonnois et al. (2001).

Fig. 9. Rate coefficients for the reaction of C4H with C2H4 as a function oftemperature, displayed on a log–log scale. The filled squares show the experi-mental results obtained in this work and the bold solid line shows the fit to thesedata. The other dashed lines represent equations used for this reaction in var-ious photochemical models of the atmosphere of Titan. The long dashed linerepresents data from Wilson and Atreya (2004), the medium dashed line fromToublanc et al. (1995) and the dotted line from Lara et al. (1996).

with a larger number of hydrocarbons will be given elsewhere(Berteloite et al., 2008, in preparation).

4.1.1. Reaction of C4H with methane (CH4), ethane (C2H6)and propane (C3H8)

The rate coefficients of the reaction of C4H with methane(Fig. 5) show a slightly positive temperature dependence asobserved by Opansky and Leone (1996a) in the case of thereaction of C2H with methane, with almost the same rate coef-ficients. This behavior indicates the presence of a small barrieralong the minimum energy path for the reaction. Fitting their re-

Reaction kinetics of the C4H radical with various hydrocarbons in the atmosphere of Titan 753

sults with an Arrhenius type function, Opansky and Leone wereable to derive an activation energy of 4 kJ mol−1 for the reac-tion C2H + CH4. As we only have data at two temperatures,298 and 200 K, it would be too risky to derive such a barrier inour case. By analogy with the reaction of C2H with methane,we believe this reaction to proceed more likely via hydrogenabstraction, C4H2 and CH3 being the two subsequent products.Given the high mixing ratio of CH4 in the stratosphere of Titan,ca. 1.4%, this reaction would represent an important way of re-cycling diacetylene. The production of the methyl radical, CH3,is also worthy of note, as the recombination of two methyl rad-icals will form ethane, the second most abundant hydrocarbonin the atmosphere of Titan.

In the cases of ethane and propane (Figs. 6 and 7), the ratecoefficients present negative temperature dependences, the ratecoefficient being larger for propane than for ethane. This neg-ative temperature dependence is consistent with reactions pro-ceeding across potential energy surfaces with no or very smallenergy barriers. The increase of the reactivity with the numberof carbons in the alkanes has already been observed in otherstudies (Murphy et al., 2003; Sims et al., 1993) and is prob-ably due to the increasing number of primary and secondaryhydrogens available in the co-reactant of C4H. As in the caseof methane, we believe the hydrogen abstraction to be the mostprobable channel, forming C4H2 and C2H5 in the reaction withethane, and C4H2 and C3H7 in the reaction with propane. Allthe reactions with alkanes presented here are therefore likely torecycle C4H2 and produce alkyl radicals.

4.1.2. Reaction of C4H with acetylene (C2H2)As for reactions involving large alkanes, we found the rate

coefficient for C4H + C2H2 to increase when the temperature islowered (Fig. 8), with rate coefficients larger than those for thereactions with alkanes. This indicates the absence of an energybarrier along the minimum energy path for the reaction. Thehigher reactivity of acetylene compared to the alkanes is proba-bly due to the presence of π electrons in C2H2. The most likelymechanism could be the addition of the electrophilic C4H tothe π orbital of C2H2, thus forming a C6H3 intermediate whichcould subsequently undergo a C–H bond fission. This reactionmechanism would be quite similar to those of the analogousC2H + C2H2 (Stahl et al., 2002) and CN + C2H2 (Huang et al.,2000) reactions. Interestingly, the structures of some C6H3 iso-mers have been recently calculated at the B3LYP/6-311G(d,p)level of calculations (Guo et al., 2007). The isomer identifiedas p3 in that paper has the correct properties to be the additionintermediate: according to the above mentioned calculations,the formation of the C6H3 addition intermediate from C4H andC2H2 would be exothermic by ca. 250 kJ mol−1, thus reinforc-ing the suggestion that an addition mechanism is possible.

The main products would be therefore, C6H2 and H. This isobviously a very interesting channel for the atmospheric pho-tochemistry of Titan, as it forms the next polyyne after C4H2,triacetylene (C6H2), so increasing the chain length of the hy-drocarbon. The formation of other products however, followingthe dissociation of the short-lived intermediate complex, C6H‡

3,cannot be completely excluded. Furthermore, the possibility of

an abstraction process, leading to the formation of C4H2 andC2H cannot be ruled out as this channel is exothermic by ca.100 kJ mol−1. It is worth noting that this abstraction channelwas not open at low temperature in the case of C2H + C2H2and CN + C2H2 as these reactions would be thermoneutral andendothermic, respectively.

4.1.3. Reactions of C4H with ethene (C2H4) andmethylacetylene (C3H4)

For these two reactions we found a similar temperature de-pendence (Figs. 9 and 7) as for the reaction with acetylene, withslightly larger rate coefficients. Again, these reactions are likelyto proceed through the addition of the electrophilic C4H radi-cal to the multiple bond of ethene, C2H4, or methylacetylene,CH3C2H, immediately followed by the formation of fragments.The hydrogen displacement channel, giving the radical C6H4in the case of ethene, and C7H4 in the case of methylacetylene,seems the most probable reaction mechanism, especially if weconsider the results of Stahl et al. (2002) on the dynamics ofC2H with hydrocarbons in crossed beam experiments. Otherchannels however, in particular an H abstraction mechanismsimilar to that occurring with saturated hydrocarbons, cannotbe ruled out.

4.2. Destruction of C4H radical by hydrocarbons in theatmosphere of Titan

In order to evaluate the efficiency of each reactant as a de-struction route of C4H the ratio of the characteristic time, τX,for the reactions of C4H with these hydrocarbons relative to thatof CH4, τCH4 , can be calculated using the observed abundancesand the rate coefficients obtained in our study. We can easilyshow that:τCH4

τX= nX

nCH4

kX

kCH4

where nX/nCH4 is the relative abundance of hydrocarbon Xwith respect to CH4 and kX and kCH4 are the rate coefficientsfor the reaction of C4H with hydrocarbon X and CH4, respec-tively. Values greater than say 0.1 for this ratio of characteristictimes will indicate that hydrocarbon X will play a significantrole in the destruction of C4H and therefore must be taken intoaccount in the photochemical scheme.

The Cassini–Huygens mission is providing very interestingnew data with respect to the composition of the atmosphere ofTitan (Flasar et al., 2005; Niemann et al., 2005; Shemanskyet al., 2005; Teanby et al., 2006, 2007; Vinatier et al., 2007;Waite et al., 2005) from which it is possible to obtain a newdescription of the concentration profiles with respect to the al-titude.

Fig. 10 is an attempt to summarize these data over the alti-tude range 120–1200 km for the hydrocarbons of interest here.Data in the stratosphere were taken from Flasar et al. (2005)and Vinatier et al. (2007). Flasar et al. measured abundances ofseveral species in the stratosphere as a function of latitude usingthe CIRS apparatus of the Cassini orbiter during fly-bys T0 andTb. Methane abundance (1.6 ± 0.5%) was obtained over the al-titude range 80–140 km whereas other hydrocarbon abundances

754 C. Berteloite et al. / Icarus 194 (2008) 746–757

m3

Fig. 10. Relative abundances of C2H2, C2H4, C2H6, CH3C2H and C3H8 withrespect to CH4 as a function of altitude in the atmosphere of Titan. Data in thestratosphere are taken from Flasar et al. (2005) and Vinatier et al. (2007) (flybyTb only). Between 600 and 1000 km, data are from Shemansky et al. (2005)and at 1200 km they are derived from Waite et al. (2005).

were derived between 140 and 180 km (Flasar et al., 2005;Waite et al., 2005). Mean abundances with respect to lati-tude were derived from their data and plotted in Fig. 10 at∼180 km. Another study by Niemann et al. (2005) based onthe GCMS instrument (Gas Chromatograph Mass Spectrom-eter) shows that methane was uniformly mixed with a molefraction of 1.41 ± 0.07% in the stratosphere. More recently,Vinatier et al. (2007) analyzed spectra obtained with CIRS dur-ing fly-bys Tb (15◦ S) and T3 (80◦ N) from which vertical pro-files were derived for a series of hydrocarbons in the altituderange 100–460 km (Tb fly-by) and 170–495 km (T3 fly-by).For clarity, in Fig. 10 we have only included their results cor-responding to the low latitudes Tb fly-by. Data from 450 to1000 km were derived from the measurements by Shemansky etal. (2005) who obtained the densities of a variety of moleculesusing the Cassini UVIS (Ultraviolet Imaging Spectrometer) ex-periment. Finally, data at ∼1200 km were extracted from thework by Waite et al. (2005) who derived abundances from theINMS (Ion Neutral Mass Spectrometer) apparatus. Note thatthe abundance taken for propane is an upper limit whereasfor ethene we chose the lowest value indicated in their pa-per.

In the altitude range that we are considering here, the tem-perature varies from about 150 to 200 K. Over this range ourrate coefficients do not vary significantly with temperature andtherefore we performed our analysis taking a mean value foreach hydrocarbon: kC2H2 = 2.2 × 10−10 cm3 molecule−1 s−1;kC2H4 = 3.0×10−10 cm3 molecule−1 s−1; kC2H6 = 0.5×10−10 cmolecule−1 s−1; kCH3C2H = 3.5 × 10−10 cm3 molecule−1 s−1

and kC3H8 = 1.5 × 10−10 cm3 molecule−1 s−1. For methane, asalready mentioned, we were not able to study its reactivity be-low 200 K. Considering that this process is very slow and thatour data indicate a reduction of the rate coefficient when thetemperature is lowered from 300 to 200 K, we have arbitrarily

Fig. 11. Characteristic reaction time τCH4 of the reaction C4H + CH4 relativeto the characteristic reaction time τX of the reaction C4H + X with X = C2H2,C2H4, C2H6, CH3C2H and C3H8 as a function of altitude in the atmosphereof Titan. Lines between data are added only for clarity.

chosen to take a rate coefficient slightly lower (and probably toohigh at 150 K) than our measurement at 200 K for the presentanalysis: kCH4 = 6 × 10−13 cm3 molecule−1 s−1.

Using these assumptions it is then possible to calculate forevery altitude the ratio τCH4/τX and therefore to analyze thepossible impact of each hydrocarbon in the destruction processof C4H. As can be seen in Fig. 11, at altitudes greater than600 km, excepting propane and methyl acetylene for which nodata are presently available, the ratio τCH4/τX is much greaterthan 1 indicating that the destruction of C4H by C2H2, C2H4and C2H6 is more efficient than that by methane. This is es-pecially striking in the ionosphere within 800 and 1000 km.These conclusions were also drawn in a recent study of thereactivity of the C2 radical with hydrocarbons (Canosa et al.,2007). In that study however, the effect was not as strikingas in the present work because reactivity of C2 + CH4 wasfound to be about 20 times higher than that of C4H + CH4.At 1200 km, reactions with C2H2 and C2H4 are still dominantwhereas the reaction with ethane becomes less efficient thanmethane although still significant (τCH4/τC2H6 ∼ 0.5). It is alsoworth stressing that the contributions of propane and methylacetylene increase significantly with respect to lower altitudes(τCH4/τC3H8 ∼ 0.06 and τCH4/τC3H4 ∼ 0.1, respectively) al-though their reaction with C4H still remains much less efficientthan that of C2H2 and especially C2H4 as a destruction sourceof C4H.

In Titan’s stratosphere, abundances of hydrocarbons aremuch smaller and therefore destruction reactions of C4H by hy-drocarbons are no longer dominant with respect to methane.It is worth noting however that τCH4/τX is close to 0.1 forC2H2 and C2H6 which are then significant destruction sourcesof C4H in this zone. On the other hand, propane, ethene andmethyl acetylene will play a minor role as the ratio τCH4/τXis only a few % or even less for these species. As mentionedabove the choice of the rate coefficient kCH may be too high

4

Reaction kinetics of the C4H radical with various hydrocarbons in the atmosphere of Titan 755

at 150 K. A rough extrapolation of our measurements down to150 K would give a rate coefficient of about kCH4(150 K) =4×10−13 cm3 molecule−1 s−1 which is not significantly differ-ent from the adopted value. Furthermore, a lower value wouldeven more emphasize the impact of other hydrocarbons than thepresent analyses and will not change our conclusions. Consid-ering the data obtained during the T3 fly-by, one can observethat the derived abundances were generally found to be largerthan those obtained from the Tb fly-by. This essentially reflectsthe polar enrichment in these high latitudes conditions result-ing from circulation in winter time. Although they are far fromcommon in Titan’s atmosphere it is interesting to point out thatthe efficiency of C2H2 in the destruction of C4H is significantlygreater than in the equatorial area and increases with altitude. At∼460 km the ratio τCH4/τC2H2 becomes close to 0.5. The effectof these peculiar atmospheric conditions for other molecules iseither insignificant (C2H6, C3H8) or not sufficient (CH3C2H,C2H4) to modify the conclusions that we indicated for the Tbfly-by data.

4.3. Comparison with rate coefficients used in variousphotochemical models

Since the pioneering model of the atmosphere of Titan byYung and coworkers in 1984 (Yung et al., 1984), various photo-chemical models have been developed, incorporating the chem-istry, some of them also adding the transport of species inthe atmosphere. The choice of the chemical scheme, and thequality of the rate coefficients used have been improved overthe years, often taking into account the latest laboratory mea-surements when available. Figs. 5–9 show the rate coefficientsused in the various photochemical models (Lara et al., 1996;Lebonnois et al., 2001; Toublanc et al., 1995; Wilson andAtreya, 2004; Yung et al., 1984) for the reactions of C4H withhydrocarbons. It can be seen that differences between predic-tions used and the measurements we made can reach severalorders of magnitude, especially at the lowest temperatures. It isworth noting that in some of these models (Yung et al., 1984;Lara et al., 1996; Toublanc et al., 1995), the authors followedthe recommendation by (Yung et al., 1984) to adjust arbitrar-ily the rate coefficients of reactions involving polyacetyleneradicals to those involving C2H using the following formula:k((C2)nH) = 31−nk(C2H). In the most recent of these modelshowever (Wilson and Atreya, 2004), the authors used the ex-perimental results obtained at low temperatures by Leone andco-workers (Hoobler and Leone, 1997, 1999; Lee et al., 2000;Murphy et al., 2003; Nizamov and Leone, 2004a; Vakhtin et al.2001a, 2001b) and Smith and co-workers (Carty et al., 2001;Chastaing et al., 1998) for the analogous reactions with C2Hin order to derive an upper limit for the production of poly-acetylene polymers. It is worth noting that if the temperaturedependence is about the same as for the reactions with C4H,the absolute rate coefficients we measured are always larger bya factor of two to four, with the exception of reactions withmethane.

4.4. The role of C4H radical for the formation of bigmolecules and haze

As mentioned in the Introduction, photochemical sourcesof hazes have been explored in various models and recentlyWilson and Atreya (2003) have considered the role of polymer-ization of pure polyacetylenes in the formation of the hazes assuggested in 1980 by Allen et al. (1980). In their photochemi-cal model, the first step for the growth of polyacetylenic chainsis given by the reaction

C2H + C2H2 → C4H2 + H,

whose rate coefficient has been measured at low temperaturesby Chastaing et al. (1998). The chain-lengthening process istherefore considered to be continued through the photolysis ofC4H2 forming polyacetylene radicals: C4H, C6H and C8H. Asmentioned in Section 4.2, the reaction of C4H with acetyleneis very likely to form efficiently triacetylene, C6H2. Reactionsof polyacetylene radicals with C4H2, C6H2 and C8H2 are pro-posed by Wilson and Atreya (2003) to lead to the formationof polyacetylene polymers. In their model, the rate coefficientsfor all these reactions were taken as equal to that of C2H +C2H2 as measured by Chastaing et al. (1998) and Leone andco-workers (Vakhtin et al., 2001a). Our results show howeverthat the rates constants for C4H + C2H2 are actually about twotimes faster. Finally, Wilson and Atreya (2003) found the con-tribution of polyacetylenes to be insignificant compared to thechannel involving aromatics for the formation of hazes and itwould be interesting to know how our new results could affecttheir conclusions. It should be mentioned however, that mostof the kinetics of aromatics considered in this photochemicalmodel have not been studied experimentally at low temperatureso far, making these results still quite speculative.

The role of metastable states of diacetylene, C4H∗2, in the

formation of large molecules in Titan’s atmosphere has alsobeen explored in the 1990’s by Zwier and Allen (1996, andreference therein). More specifically, Zwier and Allen (1996)compared the efficiency of C4H∗

2 reactions with free radicals asroutes for forming large hydrocarbons and nitriles. The main re-actions involved in their chemical scheme were the reactions ofC4H∗

2 with unsaturated hydrocarbons, the reactions of C2H withC4H2, CH4 and C2H2 and the reactions of C4H with C2H2 andCH4. At that time however, none of these reactions had beenstudied at low temperatures, and the rate constants for C2Hand C4H reactions were taken from the photochemical modelof Toublanc et al. (1995) and reference therein. As can be seenin Fig. 8, our experimental results differ from those used byToublanc et al. (1995) by an order of magnitude considering,for instance, the reaction C4H + C2H2.

The role of the metastable states of C4H∗2 in the formation

of large molecules in Titan’s atmosphere has been consideredby Vuitton et al. (2003). They determined a metastable life-time of C4H∗

2 two orders of magnitude higher than the valuecurrently used in models, but this still could not explain the dis-crepancy between models and observations. This result was oneof the motivations for this present work. Indeed, for the pho-tochemical models to reproduce the observed concentration of

756 C. Berteloite et al. / Icarus 194 (2008) 746–757

diacetylene, it would appear necessary to continue the investi-gation of its different sources and sinks.

5. Conclusion

The work presented here is, to our knowledge, the first everexperimental reaction kinetics investigation involving the radi-cal C4H. Rates of the reactions between C4H and methane werefound to be very close to those of C2H with methane, with asmall energy barrier along the minimum energy path for thereaction. For all the other reactions studied here, the rate coef-ficients are very fast (k � 10−10 cm3 molecule−1 s−1) with k

increasing when the temperature is lowered. These reactionsare therefore dominated by long range forces and proceed ona potential energy surface with no barrier or a small barrier inthe entrance channel. The rate coefficients are all larger thanthose found for reactions of C2H with the same hydrocarbons.These new rate coefficients should therefore be included in fu-ture photochemical models of the atmosphere of Titan and ofother planets containing methane. Reactions with alkanes arelikely to recycle C4H2 while other reactions could form variousproducts of interest as, for instance, triacetylene, C6H2 in thecase of the reaction involving acetylene. For the other reactionsinvolving unsaturated hydrocarbons (C2H2, C2H4, CH3C2H), ashort-lived addition complex is likely to be formed, that decom-poses to give various products with H-atom elimination beingprobably the dominant channel. The high enthalpy of forma-tion of C4H offers however, many possibilities for the products,more than is the case for C2H or CN radicals, and therefore theformation of radicals leading to larger molecules, such as PAHsfor instance. The role of these products in the formation of largeparticles and hazes should be further explored. These kinet-ics results therefore, even measured at low temperatures (40–298 K), could also be of interest for chemical schemes leadingto the formation of soot in combustion (Krestinin, 2000).

Acknowledgments

We thank the “Programme National de Planétologie,” the“Programme National Physique et Chimie du Milieu Interstel-laire,” the “Région de Bretagne,” “Rennes Métropole” and theEuropean Union (RTN Network “Molecular Universe,” Con-tract MRTN-CT-2004-512302) for support. I.R.S. gratefully ac-knowledges support for this work from the European Union viathe award of a Marie Curie Chair (Contract MEXC-CT-2004-006734, “Chemistry at Extremely Low Temperatures”). We arealso grateful to Dr. Nadia Balucani for helpful discussions onthe dynamics of the reactions presented in this paper.

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