N₂ AND CO DESORPTION ENERGIES FROM WATER ICE

The chemical structures of interstellar clouds, cloud cores, protostellar envelopes, and protoplanetary disks are all regulated by the differential freeze-out and desorption of the main carriers of oxygen, carbon, and nitrogen (Bergin & Langer 1997; Aikawa et al. 2002; Henning & Semenov 2013). The sequential freeze-out of atoms and molecules onto interstellar grains is the starting point for a rich surface chemistry that is, e.g., responsible for most of the water in space (van Dishoeck et al. 2013), as well as the abundant existence of complex, saturated molecules such as HCOOCH₃ (Garrod et al. 2008). Freeze-out also affects gas-phase compositions in multiple ways. For example, CO freeze-out is a prerequisite for abundant N₂H⁺ in molecular clouds, protostars, and protoplanetary disks (Bergin et al. 2002; Jørgensen et al. 2005; Qi et al. 2013).

The balance of freeze-out and desorption in disks also affects several aspects of planet formation. Condensation fronts in the mid planes of protoplanetary disks, so-called snowlines, can enhance the planet formation efficiency due to increased grain surface density, rapid particle growth due to cold-head effects, pressure traps, and increased grain stickiness (Ciesla 2006; Johansen et al. 2007; Gundlach et al. 2011; Ros & Johansen 2013). Snowline locations also regulate the compositions of forming planets (Öberg et al. 2011a) and planetesimals. The locations of major snowlines depend on the volatile composition (e.g., whether most nitrogen is in N₂ or NH₃), a balance between freeze-out and thermal and non-thermal desorption rates at different disk locations, and disk dynamics (Öberg et al. 2011b; Oka et al. 2012; Ali-Dib et al. 2014; Baillié et al. 2015). Two of the most important volatiles in disks (as well as in clouds and protostars) are CO and N₂. Their desorption kinetics, fundamentally set by their binding energies, will determine the locations of two of the most important disk snowlines.

CO and N₂ binding energies have been the subject of several previous studies. In two related studies, Öberg et al. (2005) and Bisschop et al. (2006) found that the binding energies of CO and N₂ in pure, layered, and mixed CO:N₂ ices were relatively similar, i.e., the ratio of the N₂ to CO binding energies were 0.93–1. These experiments did not consider the effects of water. Experiments on CO deposited on water ice has shown that CO is substantially more strongly bound in water-dominated ices compared to pure CO ices (Noble et al. 2012); Collings et al. (2003a) found a 40% higher desorption energy for CO on top of low-density amorphous water ice compare to pure CO ice. There are no similarly detailed studies of N₂ interactions with water ice, but cluster calculations suggest that N₂ may not bind very strongly to water ice (Sadlej et al. 1995). Based on those calculations N₂ desorption energies of $0.65\times {E}_{{\rm{des}}}(\mathrm{CO})$ are sometimes used in astrochemical studies (e.g., Bergin & Langer 1997). Such a low N₂ binding energy compared to CO naturally explains the presence of N₂H⁺ in cores and disks where CO has frozen out (e.g., Qi et al. 2013), but seems inconsistent with the experimentally measured small difference in binding energies of CO and N₂ in pure ices (Bisschop et al. 2006).

In this study we explore the effect of water on CO and N₂ desorption energies to astrophysically relevant ices. We aim to answer (i) whether the ratio of N₂ to CO binding energies in water-dominated ices deviate from the ratio of 0.93 found for pure ices, and (ii) whether the relative binding energies of CO and N₂ in water-dominated ices depend on the exact ice environment. In Section 2 we present the experimental method—temperature programmed desorption (TPD)—used to characterize CO and N₂ desorption. The experimental results and the derived CO and N₂ binding energies are presented in Section 3. The experimental results and their astrophysical implications are then discussed in Section 4.

TPD experiments are used to derive the desorption energies of ¹³CO or ¹⁵N₂ ices on CsI and H₂O substrates. Ices are grown by injecting molecules through a 4.8 mm diameter pipe at 0.7 inch from the substrate on a CsI window, resulting in a uniform ice. The window can be cooled to ∼11 K using a close-cycle He cryostat, and is placed in an ultra-high vacuum chamber with base pressures of <5.10⁻¹⁰ Torr at room temperature. More details on the experimental setup are given in Lauck et al. (2015). The vapor pressure of deionized water purified through at least three freeze–pump–thaw cycles using liquid nitrogen is deposited on the CsI window at (i) ∼100 K to grow amorphous compact water ice substrates, and (ii) 11 K to grow amorphous porous water ice substrates. ¹³CO (99% purity, Sigma-aldrich) and ¹⁵N₂ (98% purity, Sigma-aldrich) gases are then deposited at 11 K on top of the chosen substrate. The amount of molecules deposited is monitored during the injection using a calibrated quadrupole mass spectrometer (Pfeiffer QMG 220M1), integrating the mass spectrometer signal over time. The ice coverage is given in monolayer units with the typical approximation of 1 ML = 10¹⁵ molecules cm⁻². The chamber is also equipped with a Fourier transform infrared spectrometer (Bruker Vertex 70v) in transmission mode to monitor the amount of infrared active molecules deposited on the window in the mid-infrared. ¹³CO or ¹⁵N₂ ices of the desired thickness are then heated at a constant rate of 1 K minute⁻¹.

The temperature controller used to monitor the temperature is coupled to a thermocouple attached on a metallic window holder (Lakeshore 335). It has a relative uncertainty of 0.1 K but the absolute temperature is more difficult to assess since it depends on the thermal contact with the window holder it is attached to. We calibrated the temperature against initial CO TPD data obtained by the setup when the thermal contact was excellent (Cleeves et al. 2014), and for which the resulting CO desorption energy was within the average energy obtained in the literature (Collings et al. 2003a, 2015; Bisschop et al. 2006; Acharyya et al. 2007; Muñoz Caro et al. 2010; Martín-Doménech et al. 2014). We estimate that there is a 2 K absolute uncertainty on the temperature, based on the spread in the CO desorption energies found in the literature. The desorbing molecules are monitored using a quadrupole mass spectrometer (Hiden IDP 300, Model HAL 301 S/3) equipped with a pinhole on a translation stage that is approached 0.5 inches away from the CsI window. ¹³CO and ¹⁵N₂ isotopologues (m/z = 29 and m/z = 30 respectively) are used to rule out possible contamination in the TPD results, due to background deposition of ¹²CO and ¹⁴N₂ (m/z = 28 for both). Analysis of the TPD experiments showed that this contamination is minimal (lower than the purity percentage given by the manufacturer). The TPD plots in desorbing molecules per kelvin are obtained by subtracting the mass background for ¹³CO or ¹⁵N₂ and scaling the QMS signal so the TPD integral over the temperature range is equal to the amount of molecules deposited. This assumes that the signal detected by the QMS is proportional to the amount of molecules desorbing and that the pumping speed in the chamber is high, both of which have been verified.

The experimental data set consists of various ¹³CO or ¹⁵N₂ coverages deposited on the CsI window, on ∼50 ML_eq of compact amorphous water, and on ∼50 ML_eq of porous amorphous water. The TPD curves are fit using the Polanyi–Wigner equation:

$$\begin{eqnarray}&&-\displaystyle \frac{d\theta }{{dT}}\;=\;\displaystyle \frac{\nu }{\beta }\;{\theta }^{n}\;{{\rm{e}}}^{-{E}_{{\rm{des}}}/T},\end{eqnarray} \tag{ 1 }$$

where θ is the ice coverage, T the temperature in K, ν a pre-exponential factor in s⁻¹, β the heating rate in K s⁻¹, n the desorption order, and E_des the desorption energy in K. To derive the desorption energies, we describe the desorption kinetics using two different regimes: a multilayer regime regulated by ¹³CO–¹³CO or ¹⁵N₂–¹⁵N₂ binding energies, resulting in a zeroth-order kinetics (n = 0 in Equation (1)) and a submonolayer regime where ¹³CO or ¹⁵N₂ are in contact with the substrate, resulting in a first-order desorption. The zeroth-order regime is usually well fit by only one single desorption energy and the submonolayer regime needs to be described using a distribution of desorption energies. This is due to the different adsorption sites from a disordered and rough substrate, as reported recently by Noble et al. (2012), Collings et al. (2015), and Doronin et al. (2015), using models based on work by Redhead (1962), Koch et al. (1997), and Tait et al. (2005). For the pre-exponential factor associated with ¹³CO and ¹⁵N₂, we use the harmonic oscillator relation (e.g., Hasegawa et al. 1992; Acharyya et al. 2007; Noble et al. 2012):

$$\begin{eqnarray}&&\nu \;=\;\sqrt{\displaystyle \frac{2\;{n}_{s}\;{E}_{\mathrm{des}}}{{\pi }^{2}\;m}},\end{eqnarray} \tag{ 2 }$$

where n_s is the number of adsorption sites (∼10¹⁹ sites.m⁻²) and m is the mass of the molecule in kg. This approximation is valid in the case of small molecules like CO and N₂, but is not appropriate for large molecules, since it relies on internal and translational degrees of freedom being equivalent for the adsorbed and desorbing molecule (e.g., Müller et al. 2003). The value of the pre-exponential factor affects the derived desorption energy values, but not the ratio of CO and N₂ desorption energies, even when the factor is varied over many orders of magnitude.

The TPD curves of ¹³CO or ¹⁵N₂ on the CsI substrate, compact, and porous amorphous water are shown in Figure 1. In the top panel, ∼5 ML of ¹³CO or ¹⁵N₂ are deposited on the CsI window, then warmed up at 1 K minute⁻¹. The desorption peaks at temperatures of 24.9 K for ¹⁵N₂ and 28.2 K for ¹³CO. The shape of the curve is similar to a zeroth-order desorption with an irregular desorption tail, indicative of different submonolayer binding site on the CsI window and perhaps also the window holder. The middle panel of Figure 1 shows the TPD curves of ∼0.7 ML of ¹³CO or ¹⁵N₂ deposited on an amorphous compact thick water ice (∼50 ML) and warmed up at 1 K minute⁻¹. The curve has two peaks, which can be attributed to desorption from pure ice and desorption from the water substrate. The second peak, associated with the submonolayer interaction of the diatomic species with H₂O, is much broader than the desorption in the multilayer regime and peaks at 32.4 K for ¹⁵N₂ and at 36.6 K for ¹³CO. The bottom panel shows the TPD curves of 2 ML of ¹³CO or ¹⁵N₂ deposited on amorphous porous water. From the porous H₂O ice (${T}_{{\rm{deposition}}}$ = 11 K), ¹³CO and ¹⁵N₂ present two desorption peaks, one at 43 and 47 K, respectively, and one close to the water desorption temperature due to release of entrapped molecules (not shown here). This latter feature is due to volatile entrapment within the ice pores (e.g., Collings et al. 2003b; Bar-Nun et al. 2007; Fayolle et al. 2011; Martín-Doménech et al. 2014). 0.7 ML–0.8 ML of ¹³CO and ¹⁵N₂ desorbed below 65 K while the rest was entrapped with H₂O.

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The experiments described above clearly demonstrate that ¹⁵N₂ desorption behavior is strongly affected by the presence of water, similarly to what has previously been observed for CO. The temperature shifts between pure ice desorption from compact and porous amorphous water ice appear to be similar for the two molecules.

To better comprehend the effect of the water substrate on ¹³CO and ¹⁵N₂ desorption kinetics, we performed a series of TPD experiments for different coverages on amorphous compact water. The results are shown in the left panels of Figure 2. For high coverages above 0.7 ML, both a multilayer and a submonolayer component are present in the TPD curves. Note that the presence of a multilayer component below one monolayer could either be due to a lower surface site density than the assumed value of 10¹⁵ molecules cm⁻² or to a non-uniform wetting of the surface resulting in the formation of islands. For lower coverages, only the submonolayer desorption peak is present. For both ¹³CO and ¹⁵N₂, the submonolayer peak shifts toward higher temperatures with decreasing coverage. This coverage trend on compact amorphous water was also observed by Noble et al. (2012) for CO, who explained it by CO adsorbing first to the strongest bounding sites on the water substrate.

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To quantify the desorption energy of these systems, we fit the TPD curves using the Polanyi–Wigner equation (Equation (1) in Section 2), assuming zeroth order for the 5 ML experiments on bare CsI window. We fit the logarithm of the desorbing molecules versus the inverse of the temperature with a straight line (e.g., Doronin et al. 2015), yielding desorption energies for pure ices of 770 ± 68 K for ¹⁵N₂ and 866 ± 68 K for ¹³CO (Table 1, first row). The associated error mainly comes from the absolute uncertainty on the temperature while the relative uncertainty on the fit is less than 5 K. These desorption energy values result in pre-exponential factor values of 6.5 × 10¹¹ s⁻¹ for ¹⁵N₂ and 7.1 × 10¹¹ s⁻¹ for ¹³CO using Equation (2). Note that an empirical determination of the pre-exponential factor, using the intercept of the straight line fitting explained above, yields values of 6.6 × 10¹¹ s⁻¹ for ¹⁵N₂ and 8.0 × 10¹¹ s⁻¹ for ¹³CO, which are in good agreement with the theoretical values. The desorption energies are consistent with literature data from Öberg et al. (2005) of 790 ± 25 K and 855 ± 25 K for N₂ and CO, from Noble et al. (2012) of 828 ± 28 K for CO, and CO desorption energies from Collings et al. (2015) of 830 ± 36 K. Our N₂ desorption energy is substantially lower, however, than their measured value of 878 ± 36 K.

Table 1.  Coverages, Desorption Energy for the Pure Ice Multilayer Regime or Mean Desorption Energy with FWHM for the Submonolayer Regime on Water Substrate, and the ¹⁵N₂ to ¹³CO Desorption Energy Ratio for Various Substrates

Substrate	13CO		15N2		${E}_{{\rm{des}}}{}^{{}^{15}{{\rm{N}}}_{2}}$/${E}_{{\rm{des}}}{}^{{}^{13}\mathrm{CO}}$
	Coverage/ML	Edes/K	Coverage/ML	Edes/K
Pure ice	5.0	866 ± 68a	5.3	770 ± 68a	0.89 ± 0.02
H2O (compact)	1.3	1155 [133]	1.4	1034 [133]	0.90 ± 0.04
H2O (compact)	0.8	1180 [131]	0.7	1051 [127]	0.89 ± 0.04
H2O (compact)	0.3	1236 [139]	0.4	1090 [133]	0.88 ± 0.04
H2O (compact)	0.2	1298 [116]	0.2	1143 [113]	0.88 ± 0.04
H2O (porous)	0.7	1575 [117]	0.8	1435 [132]	0.91 ± 0.03

Note.

^aThe pure ice desorption energies are obtained by a zeroth-order fit and are given with uncertainties mainly due to the absolute error on the temperature.

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To derive desorption energies for the submonolayer regime, we used a distribution of binding energies obtained by fitting the submonolayer regime of the TPD curves by a linear combination of first-order kinetics, sampling the desorption energy by steps of 30 K between 670 and 1650 K. This technique takes into account the non-homogeneous nature of the amorphous water ice surface and has been recently used by Doronin et al. (2015) in the case of methanol adsorbed on graphite. The fitting is done in python using scipy.optimize.nnls, a non-negative least-squares fitting module, so the linear combination coefficients are kept positive. The linear combination coefficients are normalized to the initial coverages, yielding fractional coverages, and are plotted in the right panels of Figure 2 versus the sampled desorption energy. The data are smoothed using a Gaussian filter and plotted in dashed lines for clarity as well. All the distributions are close to symmetric around the mean and present FWHMs of 113–139 K, resulting in well-defined "representative" desorption energies for each coverage. The mean energy is known with a ∼30 K relative precision due to the chosen sampling energy steps (the uncertainty from the fit is smaller), and has an absolute uncertainty of 67 K. As noted for the TPD curves, the desorption distribution and their trends for various coverages are similar for ¹³CO and ¹⁵N₂. The mean desorption energy values and the FWHM are reported in Table 1. The mean submonolayer desorption energy from a compact water ice surface ranges from 1034 to 1143 K for ¹⁵N₂ and 1155 to 1575 K for ¹³CO. The shift toward higher energy for decreasing submonolayer coverages is consistent with data from Noble et al. (2012) for CO on amorphous compact water. The resulting pre-exponential factor values from Equation (2) are between 6 and 10 × 10¹¹ s⁻¹ over the sampled desorption energy range.

The desorption energies obtained for all the ¹⁵N₂ experiments are plotted versus those of ¹³CO in Figure 3. The data is consistent with a single ratio of ∼0.9 and inconsistent with a ratio of 0.65. The desorption energy ratio of ¹⁵N₂ over ¹³CO for the multilayer (pure ice) and the mean desorption energy ratio of ¹⁵N₂ over ¹³CO for the submonolayer coverages are also listed in Table 1; the values span 0.88–0.91.

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The locations of condensation fronts (snowlines) in disks, protostars and clouds depend on the desorption energies of the volatiles in question. These desorption energies increase dramatically when CO or N₂ desorbs from water ice. The highest desorption energies barriers of ∼1610 and 1470 K for CO and N₂, respectively, are achieved when CO and N₂ are deposited on a porous water ice surface where each CO or N₂ molecules can interact with multiple H₂O molecules. The large effects of water ice on the CO desorption energy was known from previous experiments (Collings et al. 2003b; Noble et al. 2012). Our study shows that N₂ is similarly affected, and both molecules are therefore likely to present ranges of thermal desorption temperatures in different interstellar and circumstellar environments. In a typical protoplanetary disk a change in desorption energy from 770 to 1435 K results in a change in N₂ snowline location from ∼50 to ∼20 AU. This estimate is based on the median temperature disk profile $T\;=\;200\;{\rm{K}}\times {(r/1\mathrm{AU})}^{-0.62}$ from Andrews & Williams (2007) and using the prescription from Hollenbach et al. (2009) to calculate the sublimation temperatures from the desorption energies. In the Solar Nebula this difference in N₂ snowline location between 50 and 20 AU is the difference between comets and the Ice Giants forming nitrogen rich or nitrogen poor (Tsiganis et al. 2005).

The second astrophysically important result of our experiments is the similarity of the N₂ and CO desorption kinetics and energies in different ice environments. Whether the ices are pure or deposited on top of different kinds of amorphous water ices, and whether the ices are more than a monolayer thick or a fraction of a monolayer, the ratio between the N₂ and CO desorption energies is consistently 0.9. This implies that in astrophysical environments where CO and N₂ ices experience similar levels of interaction with water ice, the N₂ desorption energy and temperature can always be parameterized as a fraction (0.9) of the CO desorption energy and temperature.

While the N₂-to-CO desorption energy ratio is certainly not unity, it is not close to the value of 0.65 preferred in some observational studies. In cloud cores, different formation kinetics of CO and N₂ in the gas phase may be sufficient to explain the later freeze-out of N₂, but in disks, where high densities result in short chemical timescales it is less clear that a N₂-to-CO desorption energy ratio of 0.9 is sufficient to explain observed N₂H⁺ emission exterior to the CO snowline.

It is plausible, however, that N₂ on average is interacting with a less H₂O-rich environment than CO. Garrod & Pauly (2011) finds that the H₂O abundance in ices decreases with increasing ice coverage when modeling ice formation in dark clouds, i.e., the number of H₂O molecules in a specific ice layer is less in the upper layers of the ice mantle that formed at a later time compared to the lower layers of the ice mantle. There are two reasons why N₂ ice may form slightly later than CO ice and thus be mainly present in the top-most, water-poor ice layers. First, the N₂ desorption temperature is slightly lower, which may be sufficient to keep N₂ in the gas phase at lower temperature than CO if the freeze-out timescales are long enough. Second, the nitrogen chemistry is slower compared to the CO one, which may cause N₂ ice to preferentially form later than CO ice (Hily-Blant et al. 2010; Pagani et al. 2012). Both effects could contribute to the observed CO and N₂H⁺ anti-correlation in molecular cloud cores. In disks, where the gas-phase chemistry is expected to reach steady state quickly, the different gas-phase timescales of N₂ and CO are not expected to play a role, but a slight differential freeze-out could. Differential freeze-out of CO and N₂ may also result in a high non-thermal desorption efficiency of N₂ compared to CO. Bertin et al. (2013) found that N₂ ice UV photodesorption is very efficient and CO photodesorption is quenched if a CO ice is covered by a few N₂ ice layers.

In summary, both CO and N₂ ice thermal desorption depend strongly on the ice morphology and composition. Based on our experiments, N₂ and CO desorption energies are substantially elevated, when molecules are desorbing from an amorphous water ice surface compared to a pure ice. As long as this morphology and composition are equivalent for the two molecules, the N₂ desorption energy is 0.9 that of the CO desorption energy. Differential freeze-out may increase the difference, but detailed modeling is required to assess the feasibility of this scenario.

The authors are grateful to the referee for comments and suggestions that greatly improved the manuscript. E.C.F. is supported by a Rubicon fellowship (680-50-1302), awarded by the Netherlands Organisation for Scientific Research (NWO). K.I.Ö. acknowledges funding from the Alfred P. Sloan Foundation, and the Packard Foundation.