© ESO, 2013

1. Introduction

Carbon dioxide has already been detected in the interstellar medium (ISM) by d’Hendecourt & Jourdain de Muizon already few decades ago (1989). It represents one of the most common and abundant types of ices, and many astronomical observations (by the Infrared Space Observatory and the Spitzer Space Telescope) confirm the presence of CO₂ in different environments, such as Galactic-centre sources (de Graauw et al. 1996), massive protostars (Gerakines et al. 1999; Gibb et al. 2004), low-mass young stellar objects (Nummelin et al. 2001; Aikawa et al. 2012), brown dwarfs (Tsuji et al. 2011) background stars (Knez et al. 2005), in other galaxies (Shimonishi et al. 2010; Oliveira et al. 2011), and in comets (Ootsubo et al. 2010). CO₂ is predicted to have low abundance in the gas phase (N_CO2/N_H2 = 6.3 × 10^-11; Herbst & Leung 1986), and this is confirmed by observations (van Dishoeck et al. 1996). Low abundances in gas phase, together with its observed high abundances in the solid phase, cannot be explained exclusively by formation via gas-phase schemes (Hasegawa et al. 1992), therefore surface reactions are evoked to justify a high abundance of carbon dioxide ices.

Extensive experimental studies have been carried out to study formation routes of CO₂ formation in solid-phase. Energetic routes, such as irradiation of CO ices (pure or mixed with H₂O) with photons, charged particles or electrons, have been investigated by Gerakines et al. (1996), Palumbo et al. (1998), Jamieson et al. (2006), Ioppolo et al. (2009), and Laffon et al. (2010), and have shown an efficient formation of carbon dioxide. Whittet et al. (1998), however, provided the evidence of efficient CO₂ formation in quiescent dark clouds towards the line of sight Elias 16. This suggests that the presence of CO₂ in grain mantles can also be explained through chemical pathways occurring without the addition of energy and where the radicals are thermalized with the surface. Two of these pathways are

• 1.

  CO + OH → CO₂ + H

• 2.

  CO + O → CO₂.

In recent experimental studies it has clearly been shown that reaction 1 leads to CO₂ formation, although no consistent results were obtained concerning the activation barrier: little or barrierless in Oba et al. (2011) and “high” (400 K) in Noble et al. (2011). Reaction 2 has been studied theoretically (Talbi et al. 2006; Goumans et al. 2008), and those studies suggest there is a high activation barrier (2500−3000 K). The first successful laboratory investigation of the formation of CO₂ by non-energetic processes was performed by Roser et al. (2001), who studied the surface reaction of CO and O atoms. In a first set of experiments they co-deposited the two species at 5K and performed a temperature-programmed desorption (TPD). Probably due to the low sensitivity of the quadrupole mass spectrometer they were using at that time, they did not detect any CO₂ formation. To prove the formation of carbon dioxide through such a pathway and to give a first estimate of the barrier for such a reaction they subsequently devised an experiment in which the co-deposited layer of CO and O atoms was covered by a layer of porous water ice. The TPD performed in such conditions allowed the formation of CO₂ to be detected thanks to the reaction of CO and O migrating in the interconnected pores of the amorphous ice. Under the hypothesis that the mobility of species stemmed from thermally activated processes, a reaction barrier of 290 K was obtained that explained the formation of carbon dioxide even in quiescent clouds¹. Raut & Baragiola (2011) confirmed the formation of CO₂ by Roser et al. (2011). They performed experiments showing the formation of small amounts CO₂ during co-deposition of CO and cooled O and O₂ at 20 K, although they did not provide any activation barrier for reaction 2. Here we present further experimental studies of reaction 2. CO₂ production on cold surfaces (10−40 K) was investigated by concurrent exposures of CO molecules and O atoms. The CO + O reaction is studied in a submonolayer regime on two different substrates: amorphous solid water (ASW) ice and oxidized graphite. As previously found in Raut & Baragiola (2011), CO₂ formation is in competition with O₂ and O₃ formation via the O + O and O₂ + O reaction routes. We also determined an activation energy of the CO + O reaction and the physical chemical mechanisms occurring on the surface by developing a kinetic model.

	Fig. 1 Schematic top-view of the FORMOLISM setup and the FT-RAIRS facility.
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2. Experiments

The experiments were performed with the FORMOLISM (FORmation of MOLecules in the InterStellar Medium) set-up (Fig. 1), which is described elsewhere (Amiaud et al. 2006; Congiu et al. 2012). The set-up is dedicated to investigating physical chemical reactions on surfaces of astrophysical interest, under conditions roughly similar to those encountered in the ISM. Experiments take place in an ultra-high vacuum chamber (base pressure 10^-10 − 10^-11 mbar) containing a graphitic sample surface (0.9 cm in diameter), operating at temperatures between 10 and 400 K. The temperature is controlled by a calibrated silicon-diode sensor and a thermocouple (AuFe/Chromel K-type) clamped on the sample holder. The system is equipped with a quadrupole mass spectrometer (QMS), which is used for temperature-programmed desorption (TPD) experiments. ASW ice is grown in situ on the graphite sample. The H₂O vapour is obtained from deionized water previously purified by several freeze-pump-thaw cycles carried out in a vacuum. H₂O molecules are deposited on the surface maintained at 110 K through a leak valve equipped with a micro channel doser positioned at 3.5 cm in front of the cold surface during the water ice deposition phase. The ¹³CO molecules and O atoms are sent simultaneously (co-deposition) on the surface via two triply differentially pumped beam lines. We used ¹³CO instead of ¹²CO to increase the signal-to-noise ratio of the mass signal of the CO reactant and the final CO₂ product. Hereafter we refer to ¹³CO as CO. The O atoms are produced by dissociation of O₂ molecules. The two beam lines are equipped with microwave dissociation sources (surfatron cavities delivering 200 W at 2.45 GHz) that can generate atoms by breaking molecular internal bonds. With the microwave source turned on, the dissociation efficiency of O₂ was τ = 73 ± 5% at the time of the experiments performed on ASW and 61   ±   7% when we perfomed the experiments on graphite². Atoms and undissociated molecules are cooled and instantaneously thermalized upon surface impact with the walls of the quartz tube.

We have calibrated the molecular beam as described in Amiaud et al. (2007) and Noble et al. (2012) and found that the first monolayer (1 ML = 10¹⁵ molecules cm^-2) of both ¹³CO and O₂ was reached after an exposure time of about six minutes, which therefore gives a flux φ_O2off,CO = (3.0 ± 0.3) × 10¹² molecules cm^-2 s^-1. Once the O₂ discharge is turned on, the O-atom flux is φ_O = 2τφ_O2off = 5.4 × 10¹² atoms cm^-2 s^-1 and the O₂ flux φ_O2on = (1 − τ) φ_O2off = 10¹² molecules cm^-2 s^-1. In addition, we determined that the beam did not contain O or O₂ in an excited state by tuning the ionizing electron energy inside the QMS head as described in Congiu et al. (2009).

CO₂ formation was investigated on two different surfaces, ASW and oxidized graphite. Fixed doses of O (+O₂), 0.5 ML, and CO, 0.5 ML, were deposited on the surface held at a given constant temperature. After each deposition, the surface was heated with a linear temperature ramp of 10 K/min until the adsorbate had fully desorbed from the surface (around 90−95 K). The surface was then cooled again so that a new deposition could begin at a different temperature. For both substrates (ASW ice and graphite), we used eight surface temperatures (10, 20, 30, 35, 40, 45, 50, 60 K).

We also performed an experiment to check the CO reactivity with O₂ and O₃ to form CO₂. For this purpose, we performed two sets of TPD experiments. First, the CO + O₂ reaction was checked with a set of experiments consisting of three different depositions – each one followed by TPD – with the surface temperature held at 10 K: 2 ML of CO + 2 ML of O₂ and the co-deposition of 2 ML CO and O₂. The CO + O₃ reaction was studied through a similar set of experiments except that we had previously produced ozone via the O + O₂ reaction occurring on the surface, eliminated the residual O₂ by heating to 50 K, and only then, deposited CO at 10 K.

3. Experimental results

From an energetic point of view, oxidation of CO to form carbon dioxide may proceed by the following reactions:

• 1a.

  CO + O → CO₂ (− ΔH = 532 kJ/mol)

• 2a.

  CO + O₂ → CO₂ + O (− ΔH = 33 kJ/mol)

• 3a.

  CO + O₃ → CO₂ + O₂ (− ΔH = 425 kJ/mol) ³.

To disentangle which of these reactions are effectively able to produce CO₂ on cold surfaces, we have to be sure that CO₂ is really formed on the surface and that it is not present as an impurity in the CO bottle. To check this possibility, we have performed further experiments. In Fig. 2 we show one of these tests where we checked the CO₂ presence on the graphite surface – held at 10 K – after an exposure of 4 ML of CO and after 4 ML of CO + O. The difference between the two TPDs is evident, and comparing the two CO₂ signals we find CO₂(CO dep)/CO₂(CO + O dep) ~ 8%, which confirms that the majority of the CO₂ detected is formed through surface reactions.

	Fig. 2 TPD curves of mass 45 (13CO2) between 60 and 120 K after 4 ML of 13CO exposure (dotted curve), and after 4 ML of 13CO + O (solid line) on graphite held at 10 K.
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	Fig. 3 TPD curves of mass 45 (13CO2) between 65 and 125 K after deposition of 1 ML of 13CO (squares), 13CO + O2 (circles) and 13CO + O3 (triangles) on graphite held at 10 K.
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Roser et al. (2001) and Raut & Baragiola (2011) have already studied reaction 1a, showing that this reaction can produce carbon dioxide without the intervention of energetic processes. As for reaction 2a, Mallard et al. (1994) suggested a very high activation energy barrier (~24 000 K), while reaction 3a, to the best of our knowledge, has not been studied yet. In our experimental set-up, the oxygen atom beam is produced through dissociation of O₂ molecules with a dissociation fraction which never exceeds 80%. This means that we always have an O₂ “pollution”. Moreover, when O atoms arrive on the surface, they efficiently recombine to form O₂ and O₃ (Minissale et al. 2013).

For these reasons, it is not possible to study reaction 1a without knowing how (and if) reaction 2a and 3a work. Figure 3 shows three TPD spectra of mass 45 after deposition on oxidized graphite held at 10 K of 1 ML CO, co-deposition of 1 ML CO + O₂, and 1 ML CO + O₃. The three TPD curves and integrated areas of the curves are very similar and this suggests that the CO + O₂ reaction does not occur or that at least it is very inefficient at producing CO₂ in accord with Mallard et al. (1994). We have another indication of the CO + O₂ inefficiency by comparing the area of the CO peak with and without O₂. In the two cases we do not detect any measurable variations of the CO yield. We get to the same conclusion as far as the CO + O₃ reaction is concerned. No difference can be appreciated in the comparison between the peak area of CO, of background CO₂ and of O₃. This indicates that CO + O₃ is not a fast reaction to produce CO₂ either.

In Fig. 4 we show the TPD traces resulting from irradiating ASW ice held at 20 K with 0.5 ML of CO + O (i.e., 0.5 ML CO, 0.15 ML O₂, 0.7 ML O). Four main peaks appear at masses 29, 32, and 45. The mass-29 peak is clearly due to the CO desorption, which occurs between 32 K and 55 K and peaks at 41 K. Mass 32 presents two peaks, the first one between 28 and 42 K – peaked at 34 K – is due to O₂ desorption while the second one peaking at around 65 K included between 55 K and 75 K is due to the desorption of O₃ detected in the form of O fragments, as a result of the O₃ cracking in the head of the QMS. We are certain that this peak comes from O₃ desorption because we also detect the signal at mass 48, which has the same shape, though less intense, of the one at mass 32 in the same temperature range (not shown). Finally, the tiny high-temperature peak also shown in the insert comes from to the CO₂ desorption occurring between 75 and 95 K and peaking at 83 K.

	Fig. 4 TPD curves at mass 29, 32, and 45 after irradiation of 0.5 ML of 13CO + O on ASW ice held at 20 K. Four peaks are visible. The first peak between 28 K and 42 K is due to O2 desorption, the second one between 32 and 55 K is due to 13CO desorption. The third peak between 55 K and 75 K represents O3 desorption, while the high-temperature peak is the desorption of 13CO2 (75−95 K).
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The results of the other set of experiments are very similar to the one just described. In fact, we observe always four peaks (except for the 50 K experiment, where O₂ has already desorbed before starting the TPD), but their intensities change with temperature as shown below. Figure 4 indicates that two molecules are actually formed on the surface, O₃ and CO₂. Moreover, O₂ can also be either formed on the surface via the O + O reaction or come from the beam because of the non-total dissociation of O₂ molecules. Considering all reactants and products and remembering that reactions 2a and 3a can be disregarded, the possible reactions occurring on the surface are listed below:

• 1a.

  CO + O → CO₂

• 4a.

  O + O → O₂

• 5a.

  O + O₂ → O₃

• 6a.

  O + O₃ → 2 O₂.

The last three reactions were studied in Minissale et al. (2013). While reactions 4a and 5a seem to be barrier-less (or with a very low activation barrier below 190 K/k_b), reaction 6a does not occur and is likely to have a high activation barrier (see Table 1).

Fig. 5 13CO2 yield as a function of surface temperature during deposition of 0.5 ML of 13CO + O. Circles represent the integrated area under the TPD curves of mass 45 after a deposition of 0.5 ML of 13CO + O on ASW ice held at different temperatures (10 K, 20 K, 30 K, 35 K, 40 K, 45 K, 50 K, 60 K). The solid line is a fit of the area behaviour. The TPD peaks (obtained at Tsurface = 20 K) added in the figure show when O2 and 13CO desorb, and this helps interpret the 13CO2 yield behaviour with temperature.

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Apparently, reaction 1a is in competition with reactions 4a and 5a. To understand how efficiently the CO + O reaction proceeds and to derive its activation barrier, we performed several experiments at a fixed coverage and by varying the surface temperature. Temperature, in fact, affects both oxygen atom diffusion and the desorption of species and these two processes give us the key to understand our results (Figs. 5 and 6) and consequently the way CO₂ is formed.

Fig. 6 O2 and O3 yields as a function of surface temperature during deposition of 0.5 ML of 13CO + O. The circles and the squares represent the integrated area under the TPD curves of O2 and O3, respectively, after deposition of 0.5 ML of 13CO + O on ASW ice held a different temperatures (10 K, 20 K, 30 K, 35 K, 40 K, 45 K, 50 K, 60 K). The solid line is a fit of the area behaviour. The added O2 TPD (obtained at Tsurface = 20 K) helps interpret the O3 yield behaviour with temperature.

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As we can see in Fig. 5, the CO₂ signal is already present at 10 K⁴, and it reaches a maximum when the surface temperature during exposure is 35 K. Subsequently, for higher temperatures the CO₂ signal decreases and becomes zero at 60 K. This behaviour can be explained by considering three different “temperature zones”: below 30 K, between 30 K and 35 K, and higher than 35 K. In the range between 10 K and 30 K, the majority of oxygen atoms are used to produce ozone (Fig. 6) via reaction 4a and 5a, and its production rises with temperature owing to the increase in O diffusion. In this low-temperature zone, only a small amount of oxygen atoms is used to produce CO₂, probably via the Eley-Rideal mechanism, see below. When O₂ starts to desorb (mid-temperature zone, 30−35 K) O atoms have a lower probability of meeting O₂ molecules to form O₃. In fact, we see a decrease in the amount of O₃ desorbed (Fig. 6), while in this range of temperature the probability that an oxygen atom encounters a CO molecule increases (as a consequence of the reduced coverage of O₂). At temperatures higher than 35 K, CO desorption begins and the CO₂ signal begins to drop with same pattern observed for ozone. This suggests that also at high temperatures (45−50 K) molecules and atoms coming from the beam still have a residence time on the surface long enough to react and form appreciable amounts of ozone and CO₂. The shape of the CO₂ and O₃ yields in Figs. 5 and 6 suggest that CO₂ formation is limited by O₂ molecules or, in other words, that reaction 1a is in competition with reactions 4a and 5a. In fact, only when the O₃ signal decreases (and O₂ desorbs) CO₂ formation rises. However, presence of O₂ apart, CO₂ always forms in small amounts, and this very probably indicates the existence of an activation barrier (hereafter E_a) for the reaction CO + O. To evaluate E_a and to understand what surface mechanisms are responsible for CO₂ formation we have developed a model described in the next section.

4. Model

In this section we present the model used to fit our experimental data. It is composed of two sets of differential equations. Reactions 1a, 4a, and 5a can occur through two mechanisms: the Eley-Rideal (ER) and the Langmuir-Hinshelwood (LH) mechanisms. In the ER mechanism one molecule is already adsorbed on the surface and the other comes from the gas phase (i.e., the beam line). In the LH mechanism, both molecules are bound to the surface and by diffusion they can meet each other and react. We consider five species: two are coming exclusively from the beam, O atoms and CO molecules, two are formed only on the surface, O₃ and CO₂, and one, O₂, is coming both from the beam and formed on the surface. Below the list of equations governing the CO₂ formation by the ER mechanism follows: where capital-element symbols express the surface densities (expressed in fraction of ML) of the species, τ is the dissociated fraction of O₂ defined in Sect. 2, φ_O2off,CO are the fluxes (0.003 cm^-2 s^-1) of O₂ and CO respectively, r_aER is the reaction probability of CO + O via ER, and ϵ is the evaporation probability – due to chemical desorption – of O₂ formed on the surface. Simple calculations give that 2τφ_O2off and (1 − τ)φ_O2off are the O and O₂ flux respectively when the discharge is on. Similarly, as for the CO₂ formation by the LH mechanism, we have: where capital element symbols express the surface densities (expressed in ML) of the species, k is the diffusion coefficient of O atoms (the unit of k is ML^-1 s^-1, that can be transformed in the usual unit cm² s^-1 by considering that 1 ML = 10¹⁵ molecules cm^-2), r_aLH has the same physical meaning of r_aER, but in the case of LH reactions, Des_O2,CO are functions that take into account O₂ and CO desorption. These two functions are expressed through the first-order Polanyi-Wigner equation (11)where ν is the “attempt frequency” (s^-1) for overcoming the barrier to desorption, and E_O2,CO are the activation energies for desorption of O₂ and CO respectively. Our experimental data provide the fraction of ML of each species present on the surface, therefore in this two sets of equation we have six free parameters: r_aER,LH, E_O2,CO, ϵ and k. Actually, four of these parameters have already been studied under very similar experimental conditions (ϵ in Dulieu et al. 2013; k in Minissale et al. 2013, E_O2,CO in Noble et al. 2012), hence by using their measured values we can reduce to two the number of free parameters, namely, r_aER, and r_aLH; ϵ is equal to zero in the case of a water ice surface while it is 0.5 if the experiments are carried out on graphite. The diffusion coefficient k is a function of the temperature and we describe it using the law k = k₀(1 + ), where k₀ is 0.9 and T₀ is 10 K. Finally, the E_O2 and E_CO desorption barriers are two energy distributions centred at 1310 K/k_b and 1430 K/k_b respectively. In our model, we could have added another couple of parameters, k_O2,CO, representing the O₂ and CO diffusion. However, O diffusion is always dominant with respect to O₂ or CO diffusion. The addition of O₂ and CO diffusion would cause a quicker consumption of O atoms, without significant changes of the final amount of species. Introducing two more free parameters would then be of secondary importance for the purpose of this work and it would add more complexity. For these reasons we have chosen to neglect the diffusion of O₂ and CO.

	Fig. 7 Model results for CO2 production on ASW (pure ER). The curves in this figure were obtained by using rLH = 0, and different rER values (ranging from 0.005 to 0.1). The squares are a best fit of the experimental values.
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	Fig. 8 Model results for CO2 production on ASW (pure LH). The curves in this figure were obtained by using rER = 0, and different rLH values (ranging from 0.001 to 0.02). The squares are a best fit of the experimental values.
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To find the best fit of our experimental values, we have proceeded in this way: we set one of the two parameters to zero and vary the other between 0 and 1. We thus find a value that reproduces the experimental CO₂ yield at 10 K and that at once does not overcome the other experimental CO₂ yields. This value will be an upper limit. In the case of r_aER, a value higher than 0.05 returns too much CO₂ (Fig. 7) while in the case of r_aLH, the upper limit is around 0.002 (Fig. 8). Then, through the χ² test – here we compare the simulated outcome to the experimental values – we have found that the best couple of reaction probabilities is r_aER = 0.021 and r_aLH = 0.0019. The model results showing the yields of all species are displayed in Fig. 9. To find acceptable solutions we need concentrate on the CO₂ curve. In fact, the reaction probabilities are the only free parameters of our model and one small variation of them strongly affects the CO₂ curve (r_a appears in each term of the CO₂ equations), that is why the experimental CO₂ yields are the most important constraints in our model. Moreover, the model allows us to distinguish and quantify the contribution to CO₂ formation by either ER or LH mechanism.

	Fig. 9 Model results for all species on ASW. The curves in this figure were obtained by using rLH = 0.0019 ± 0.0005 and rER = 0.021 ± 0.007. The circles, stars, triangles and squares represent O2, CO2, CO, and O3 experimental results respectively. The inset displays a magnified view of the CO2 yield around its maximum for clarity.
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In Fig. 10 we show the individual contributions to CO₂ formation by ER or LH mechanism as a function of surface temperature. In Table 2 the CO₂ yield is expressed in monolayers, in units of the normalized amount formed at 10 K, and in fractions of the total carbon dioxide formed. CO₂ formation via ER mechanism appears to be constant with temperature between 10 and 40 K also because, in theory, this mechanism is temperature independent. At higher surface temperatures, however, ER starts to be inefficient because of the desorption and the decrease of the residence time of species on the surface, thus the CO₂ production efficiency by this mechanism drops off. On the contrary, the LH mechanism depends on the surface temperature and its efficiency increases going from 10 to 40 K owing to the favoured diffusion of atoms. Beyond 40 K, as occurs for the ER case, the probability that O atoms and CO molecules leave the surface is high and the CO₂ yield decreases fast with temperature. The ER and LH contribution to CO₂ formation is approximately equal at low temperatures (below 20 K), while at high temperatures most CO₂ is formed via the LH mechanism. This is not surprising considering the power law dependence on the temperature of the diffusion parameter.

	Fig. 10 Model results showing the contribution to CO2 formation by either ER (triangles) or LH (circles) mechanism. Contributions to CO2 formation are expressed in monolayers (ML) as a function of surface temperature.
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4.1. Evaluation of the CO + O barrier

The two reaction probabilities r_aER and r_aLH give the probability that the CO + O reaction occurs, thus they have the same physical meaning and can be used to evaluate other physical quantities. By inverting a normalized Arrhenius equation the desorption energy E_a can be calculated as follows: (12)Two alternative strategies can be used to evaluate the activation barrier of the reaction; we can derive the reaction barrier E_a either from r_aER or r_aLH.

4.1.1. ER case

In collision theory, this law is derived by considering gas phase particles described through a Maxwell-Boltzmann (MB) energy distribution and assuming that the interactions between the reactants can occur only via head-on collisions (see Atkins 2006). For ER reactions, the use of Eq. (12) is plausible because the interactions occur between a particle coming from the gas phase (MB distribution) and a particle thermalized with the surface. In this case, somehow similarly to gas phase reactions, the impinging particles either collide and react with one adsorbate or have enough energy to hop on the surface before thermalizing and accommodating in an empty adsorption site. Gas phase molecules coming from the beam-line are at around T_gas = 300 ± 20 K/k_b while the target particles adsorbed on the substrate are thermalized with the surface at T_solid = 10 − 60 K/k_b. The temperature in Eq. (12) represents the average molecular (atomic) kinetic energy () and in a gas at the thermodynamic equilibrum, is proportional to the thermodynamic temperature. The problem is to know the exact temperature (T_eff) to insert in Eq. (12). We consider three different cases:

• K

• K.

• K.

Evidently, we do not take into account the case T_eff = T_solid, because that means to consider molecules already thermalized with the surface, as in a pure LH process.

In the first case (T = T_g = 300 K) we obtain a barrier of 1200 K/k_b. Clearly, in our experiments we cannot consider CO and O as two gases at the same thermodynamic equilibrium so the temperature is likely to be lower than 300 K. This means that E_a = 1200 K/k_b is to be considered only an upper limit of the activation barrier.

The second and third cases are T_eff = 202, 123 K. This choice is justified by the equation below⁵(13)where μ is the effective mass of the CO and O system. These temperatures correspond to the velocity of the centre of mass of the system. By substituting their values in Eq. (12), we find a CO + O reaction barrier between E_aER = 780–475 K/k_b.

4.1.2. LH case

As stated above, we have also tried to derive the reaction barrier from r_aLH.

In general, the activation barrier of a process or reaction is the same independently of the mechanism that led to it. As to the LH mechanism, reaction partners adsorbed in the same site collide at the temperature (velocity) of the substrate; the disadvantage with respect to overcoming the barrier in the ER case is the lower energy of the colliding partners, but with the advantage that they will collide ν times per second (usually ν = 10^12 − 13 s^-1) instead of only once.

It should be noted that r_LH is dependent on the temperature even though we have given a unique value of the reaction probabilities⁶. The temperature dependence of r_LH is not as simple as in the Arrhenius case (Eq. (12)). In addition, it cannot be derived from the experimental values because they do not provide enough constraints, hence we give a mean value across the whole temperature range investigated (10−60 K). We then try to estimate the reaction barrier by taking into account the two following considerations:

• i)

  although O-atoms diffusion is predominant with respect to that of O₂ and CO, at high temperatures⁷ also O₂ and CO diffusion has to be taken into account if a proper evaluation of r_LH(T) is required.

• ii)

  Non-exponential behaviour of the CO₂ formation rate due to occurrence of tunneling at very low temperatures (Goumans & Andersson 2010, see Fig. 11).

  	Fig. 11 Temperature dependence of rLH(T) between 10 and 60 K. The two pinstriped regions indicate how a different parametrization of tunneling for CO + O reaction and of O2 and CO diffusion can change our estimation of rLH(T). The dashed line represents our experimental data. Full circles are an example of a pure Arrhenius behaviour.
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These considerations suggest that r_LH(T), for T < 25 K, is better described by this law (14)where r_tunn(E_a,T) (it is ≥0) represents the rate of tunneling of the CO + O reaction and it is able to increase the reaction probabilities value at low temperature. By inverting Eq. (14) we have (15)By putting T_eff = 25 K in Eq. (15), r_LH(25 K) = 0.0019 and r_tunn(E_a,T) = 0, thus and we obtain a lower limit for E_a of 160 K/k_b. This value is underestimated for two reasons:

• At 25 K the tunneling term could become to be dominant with respect to the classical one (Arrhenius law), and clearly is not zero.

• is a mean value, and very probably r_LH(T) presents a minimum around 25 K.

This means that r_LH(25 K) ≪ 0.0019 and E_a ≫ 160 K/k_b are consistent with the values obtained for r_ER.

4.1.3. Conclusions

We have described above how we evaluated the activation barrier of the CO + O reaction. Our model allows us to distinguish which mechanisms (Eley Rideal or Langmuir-Hinshelwood) is at play in different temperature regimes and we are able to give a range of values of the activation barrier of reaction CO + O of 780−475 K/k_b (see Table 3). We have to note that these values make sense only in the range of validity of Eq. (12). Our results are summarized in Table 3. Finallly, it should be noted that the range of activation energy barriers given in this work are only apparently inconsistent with the 290 K/k_b value of Roser et al. 2001, which can actually be considered one of the diverse cases addressed in the present paper. In fact, they provide an estimation (not a measure) of the barrier by using only the classical LH mechanism (very low T_eff) (on the other hand the ER mechanism (high T_eff) with the same barrier would produce more CO₂ than that they observed.). Their estimate can thus be considered a lower limit of the barrier which is included in our study of the LH case (lower limit =160 K/k_b).

5. Astrophysical conclusions

In this paper we have shown that CO₂ can be formed by the CO + O reaction on cold surfaces, such as amorphous water or oxidized graphite. This reaction is relevant to astrochemistry in that it may explain CO₂ formation on interstellar dust grains by surface reactions and thus justifies its abundance in the solid phase. As mentioned in the introduction, the CO + O reaction competes with the CO + OH reaction (some experimental works have already been conducted by Ioppolo et al. 2013), another non-energetic route to CO₂ formation in space. The CO + OH pathway seems to be facilitated by the low barrier of the reaction, but it has an other type of hindrance. In fact, it requires OH formation first (see Chaabouni et al. 2012; Cuppen et al. 2010, and references therein for details on OH formation in space). In H-rich environments, OH can be formed easily, although it can be very quickly destroyed to form water. These facts suggest that the CO₂(CO + O)/CO₂(CO + OH) ratio strongly depends on three parameters:

• the O/H ratio, very probably the most important parameter;

• the grain temperature: the higher it is the shorter is the H residence time on the grain and thus the probability of OH formation;

• H and O diffusion on the surface: since only the first one is usually considered in models (e.g., Garrod & Pauly 2011), the CO + O contribution is, in our opinion, underestimated.

In conclusion, the CO + O pathway seems to be important in those astrophysical environments where a lack of UV photons forbids the energetic routes leading to CO₂ or in environments with large abundances of atomic oxygen. Although the abundance of O atoms in ISM remains controversial, the detected high abundances of solid CO₂ together with observations of atomic oxygen in the molecular cloud Taurus⁸ (Whittet et al. 1998), Sgr B2, and L1689N2⁹ (Charnley & Kaufman 2000; Caux et al. 2001), make these environments a good example of where the CO + O reaction can efficiently proceed to form CO₂.

Acknowledgments

The LERMA-LAMAp team in Cergy acknowledges the support of the national PCMI programme founded by CNRS, the Conseil Regional d’Ile de France through SESAME programmes (contract I-07-597R). M.M. acknowledges financial support by LASSIE, a European FP7 ITN Community’s Seventh Framework Programme under Grant Agreement No. 238258. We also thank the anonymous referees for the fruitful suggestions. F.D. and M.M. thank Prof. H. T. Diep for fertile discussions.

References

Appendix A: Equation (13) derivation

The molecules in a gas at ordinary temperatures (i.e. at room temperature) can be considered to be in ceaseless, random motion at high speeds. The average translational kinetic energy for these molecules can be deduced from the Boltzmann distribution. In a gas at the temperature T_gas, it can be expressed for one molecule by the following equations, (A.1)where v_x and m_x are velocity and mass of the particle x, k_b is the Boltzmann constant.

Our case is just a little bit more complex. We can consider the O + CO system as a two-body problem. We define the reduced mass – the effective inertial mass of the system – as follows (A.2)and the relative velocity (A.3)by taking the square of the relative velocity and by doing the average we obtain (A.4)where ⟨2v₁·v₂⟩ = 0 because of the isotropy of v₂.

In the simplest case (m₁ = m₂ and all the particles are at T_gas) through the equation below (A.5)it is possible to find the effective temperature of the molecules (A.6)In the case (our case) of two different molecules (i.e. CO and O, m_CO ≠ m_O) at different temperatures (T_CO = T_solid ≠ T_gas = T_O or T_O = T_solid ≠ T_gas = T_CO), we will have a reduced mass of (A.7)then, in the case of CO adsorbed and O arriving from the gas phase, or, in the case of O adsorbed and CO from gas phase, and so From these equations, by using T_solid = 25 K and T_gas = 300, we obtain These two T_eff will be used to find a lower and an upper limit for the activation barrier. We have to note that the two reactions O_gas + CO_solid and CO_gas + O_solid do not have the same probability of occurring at different temperatures due to a different residence time on the surface and diffusion constant of molecules and atoms and, in the case of O_solid strong concurrence with O + O₂ reaction. This consideration induces us not to give an exact value of the activation barrier, but just a possible range of values.

All Tables

All Figures

	Fig. 1 Schematic top-view of the FORMOLISM setup and the FT-RAIRS facility.
Open with DEXTER
In the text

	Fig. 2 TPD curves of mass 45 (13CO2) between 60 and 120 K after 4 ML of 13CO exposure (dotted curve), and after 4 ML of 13CO + O (solid line) on graphite held at 10 K.
Open with DEXTER
In the text

	Fig. 3 TPD curves of mass 45 (13CO2) between 65 and 125 K after deposition of 1 ML of 13CO (squares), 13CO + O2 (circles) and 13CO + O3 (triangles) on graphite held at 10 K.
Open with DEXTER
In the text

	Fig. 4 TPD curves at mass 29, 32, and 45 after irradiation of 0.5 ML of 13CO + O on ASW ice held at 20 K. Four peaks are visible. The first peak between 28 K and 42 K is due to O2 desorption, the second one between 32 and 55 K is due to 13CO desorption. The third peak between 55 K and 75 K represents O3 desorption, while the high-temperature peak is the desorption of 13CO2 (75−95 K).
Open with DEXTER
In the text

	Fig. 5 13CO2 yield as a function of surface temperature during deposition of 0.5 ML of 13CO + O. Circles represent the integrated area under the TPD curves of mass 45 after a deposition of 0.5 ML of 13CO + O on ASW ice held at different temperatures (10 K, 20 K, 30 K, 35 K, 40 K, 45 K, 50 K, 60 K). The solid line is a fit of the area behaviour. The TPD peaks (obtained at Tsurface = 20 K) added in the figure show when O2 and 13CO desorb, and this helps interpret the 13CO2 yield behaviour with temperature.
Open with DEXTER
In the text

	Fig. 6 O2 and O3 yields as a function of surface temperature during deposition of 0.5 ML of 13CO + O. The circles and the squares represent the integrated area under the TPD curves of O2 and O3, respectively, after deposition of 0.5 ML of 13CO + O on ASW ice held a different temperatures (10 K, 20 K, 30 K, 35 K, 40 K, 45 K, 50 K, 60 K). The solid line is a fit of the area behaviour. The added O2 TPD (obtained at Tsurface = 20 K) helps interpret the O3 yield behaviour with temperature.
Open with DEXTER
In the text

	Fig. 7 Model results for CO2 production on ASW (pure ER). The curves in this figure were obtained by using rLH = 0, and different rER values (ranging from 0.005 to 0.1). The squares are a best fit of the experimental values.
Open with DEXTER
In the text

	Fig. 8 Model results for CO2 production on ASW (pure LH). The curves in this figure were obtained by using rER = 0, and different rLH values (ranging from 0.001 to 0.02). The squares are a best fit of the experimental values.
Open with DEXTER
In the text

	Fig. 9 Model results for all species on ASW. The curves in this figure were obtained by using rLH = 0.0019 ± 0.0005 and rER = 0.021 ± 0.007. The circles, stars, triangles and squares represent O2, CO2, CO, and O3 experimental results respectively. The inset displays a magnified view of the CO2 yield around its maximum for clarity.
Open with DEXTER
In the text

	Fig. 10 Model results showing the contribution to CO2 formation by either ER (triangles) or LH (circles) mechanism. Contributions to CO2 formation are expressed in monolayers (ML) as a function of surface temperature.
Open with DEXTER
In the text

	Fig. 11 Temperature dependence of rLH(T) between 10 and 60 K. The two pinstriped regions indicate how a different parametrization of tunneling for CO + O reaction and of O2 and CO diffusion can change our estimation of rLH(T). The dashed line represents our experimental data. Full circles are an example of a pure Arrhenius behaviour.
Open with DEXTER
In the text