# Thermal desorption of formamide and methylamine from graphite and amorphous water ice surfaces

Henda Chaabouni, Stephan Diana, T. Nguyen, François Dulieu

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Henda Chaabouni, Stephan Diana, T. Nguyen, François Dulieu. Thermal desorption of formamide and methylamine from graphite and amorphous water ice surfaces. Astronomy and Astrophysics - A&A, 2018, 612, pp.A47. 10.1051/0004-6361/201731006. hal-01918175

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# Thermal desorption of formamide and methylamine from graphite and amorphous water ice surfaces

H. Chaabouni, S. Diana, T. Nguyen, and F. Dulieu

LERMA, Université de Cergy-Pontoise, Observatoire de Paris, PSL Research University, Sorbonne Université, UPMC Univ. Paris 06, UMR 8112, CNRS, 5 mail Gay Lussac, 95000 Cergy-Pontoise, France
e-mail: Henda.Chaabouni@u-cergy.fr, Francois.Dulieu@obspm.fr

Received 18 April 2017 / Accepted 27 December 2017

## ABSTRACT

*Context.* Formamide (NH₂CHO) and methylamine (CH₃NH₂) are known to be the most abundant amine-containing molecules in many astrophysical environments. The presence of these molecules in the gas phase may result from thermal desorption of interstellar ices.

*Aims.* The aim of this work is to determine the values of the desorption energies of formamide and methylamine from analogues of interstellar dust grain surfaces and to understand their interaction with water ice.

*Methods.* Temperature programmed desorption (TPD) experiments of formamide and methylamine ices were performed in the sub-monolayer and monolayer regimes on graphite (HOPG) and non-porous amorphous solid water (np-ASW) ice surfaces at temperatures 40–240 K. The desorption energy distributions of these two molecules were calculated from TPD measurements using a set of inde-pendent Polanyi–Wigner equations.

*Results.* The maximum of the desorption of formamide from both graphite and ASW ice surfaces occurs at 176 K after the desorption of H₂O molecules, whereas the desorption profile of methylamine depends strongly on the substrate. Solid methylamine starts to desorb below 100 K from the graphite surface. Its desorption from the water ice surface occurs after 120 K and stops during the water ice sublimation around 150 K. It continues to desorb from the graphite surface at temperatures higher than 160 K.

*Conclusions.* More than 95% of solid NH₂CHO diffuses through the np-ASW ice surface towards the graphitic substrate and is released into the gas phase with a desorption energy distribution *E*<sub>des</sub> = 7460–9380 K, which is measured with the best-fit pre-exponential factor *A* = 10¹⁸ s⁻¹. However, the desorption energy distribution of methylamine from the np-ASW ice surface (*E*<sub>des</sub> = 3850–8420 K) is measured with the best-fit pre-exponential factor *A* = 10¹² s⁻¹. A fraction of solid methylamine monolayer of roughly 0.15 diffuses through the water ice surface towards the HOPG substrate. This small amount of methylamine desorbs later with higher binding energies (5050–8420 K) that exceed that of the crystalline water ice (*E*<sub>des</sub> = 4930 K), which is calculated with the same pre-exponential factor *A* = 10¹² s⁻¹. The best wetting ability of methylamine compared to H₂O molecules makes CH₃NH₂ molecules a refractory species for low coverage. Other binding energies of astrophysical relevant molecules are gathered and compared, but we could not link the chemical functional groups (amino, methyl, hydroxyl, and carbonyl) with the binding energy properties. Implications of these high binding energies are discussed.

**Key words.** methods: laboratory: molecular – molecular processes – astrochemistry – techniques: spectroscopic – ISM: molecules – dust, extinction

## 1. Introduction

Formamide, NH₂CHO, is a species of great relevance in prebiotic chemistry (Saladino et al. 2012; Barone et al. 2015). This species contains a (quasi) peptide bond (–NH–(C=O)) that is very active in the synthesis of nucleic acid bases, carboxylic acids, sugars (Saladino et al. 2012), and amino acids responsible for the formation of proteins. It is also well known to be the precursor species for the formation of purine and pyrimidine bases during the course of chemical evolution leading to the origin of life (Bhushan et al. 2016). Formamide has been observed in the gas phase in several astronomical environments, such as prestellar and protostellar objects (Kahane et al. 2013), massive hot molecular cores (Bisschop et al. 2007), hot corinos (López-Sepulcre et al. 2015), and comets, such as C/20012 F6 (Lemmon), C/2013 R1 (Lovejoy) (Biver et al. 2014), and Hale-Bopp (Bockelée-Morvan et al. 2000).

Formamide has been once tentatively identified in interstellar ices of star-forming regions by ISO-SWS infrared spectra

(Raunier et al. 2004), but it is no longer in the list of confirmed molecules in interstellar ices (Boogert et al. 2015). As for numerous molecules, especially interstellar complex organic molecules, astrochemists would like to put constraint on the formation pathway of formamide. In order to discriminate different scenarios of star formation, solid-state and gas-phase formation routes are usually debated because they imply different physical conditions. For both chemical routes, there are arguments coming from observations and others belonging to the physical or chemical properties of NH₂CHO. On the observational side, López-Sepulcre et al. (2015) have noticed that NH₂CHO is correlated to isocyanic acid (HNCO) abundances. Furthermore, the first detection of deuterated formamide towards the low protostar IRAS 16293 by ALMA-PILS, which was a D/H ratio of 2% similar to HNCO (Coutens et al. 2016), has been found to be in agreement with the hypotheses that these species are chemically related through grain-surface formation. On the other hand, Codella et al. (2017) have explained well the observation of formamide in the brightest shocked region of the
large-scale molecular outflow L157-B1 through the gas-phase
reactions between NH₂ and H₂CO. For prestellar core condi-
tions (*T* < 10 K), despite the inclusion of this very efficient
reaction in their chemical network, Vasyunin et al. (2017) do not
really overestimate the abundance of formamide in the prestellar
core L1544. In these cold prestellar sources, formamide remains
undetected according to Jiménez-Serra et al. (2016). The sce-
nario of the gas-phase formation route of formamide relies on the
computational work of Barone et al. (2015) and that of Skouteris
et al. (2017), who studied the deuteration aspects and confirmed
that the gas-phase route for the formation of formamide in the
first cold prestellar phase is in agreement with the observa-
tions. The theoretical discussion (Song & Kästner 2016) about
the presence or the absence of the barrier for this key reac-
tion (NH₂ + H₂CO → NH₂CHO + H) in the gas phase will end
when experimental work is carried on. On the other hand, in
the solid state, many experimental reports about the formation
of formamide have been published. Energetic electron bombard-
ment of CO–NH₃ ice mixtures (Jones et al. 2011), ion irradiation
of H₂O–HCN ices at 18 K (Gerakines et al. 2004), and during the
warm-up of photolyzed ice mixtures of H₂O, CH₃OH, CO, and
NH₃ (Bernstein et al. 1995), led to the formation of NH₂CHO.
Recent laboratory experiments of Fedoseev et al. (2016) have
also produced formamide molecules by hydrogenation and UV
photolysis of NO in CO-rich interstellar ice analogues. The
chemical link in the solid phase of HNCO and NH₂CHO has
been ruled out by H-bombardment experiments of HNCO at low
surface temperature (Noble et al. 2015), which do not lead to
detectable amounts of NH₂CHO molecules. Our group demon-
strates that formamide can be produced with high efficiencies
even without the help of external energy (Nguyen et al., in prep.).
A last aspect of the solid phase chemical route concerns the
binding energy of formamide. Dawley et al. (2014) have inves-
tigated thermal desorption of thick mixed H₂O–NH₂CHO ices
on a silicate (SiO₂) grain analogue from 70 to 400 K. These
authors have observed a delayed desorption peak of the water
ice at 160–200 K, resulting from the diffusion of H₂O molecules
during the phase transition of formamide accumulated in the
ice, followed by a large desorption profile at higher tempera-
tures (200–380 K), corresponding to the diffusion of molecules
through the high surface area of silicate. The desorption activa-
tion energy of formamide measured experimentally from SiO₂
substrate has been found to be 14.7 kcal mol⁻¹ (or 7397 K) with
a pre-factor *A* = 10¹³ s⁻¹. Recently, Wakelam et al. (2017) have
estimated the binding energy of formamide on water ice sur-
face to be (6300 ± 1890) K using a semi-empirical theoretical
approach. The discrepancy can obviously come from the cal-
culation method, but could also find its origin in the amount
of NH₂CHO interacting with the water ice, which is high in
the first case (Dawley et al. 2014) and very low in the second
case (Wakelam et al. 2017). Experiments performed with thin
layers on the surface of the substrate are required for a bet-
ter comparison. Anyhow, formamide has a very high value of
binding energy that is much higher than that of H₂O, which
is around 4930 K for crystalline water ice, estimated from the
results of Fraser et al. (2001) using a pre-exponential factor
*A* = 10¹² s⁻¹. At the current state of the astrochemistry, it is
not mandatory to involve the direct formation of formamide
on dust grains to explain its observation (or non-observation)
in various media, as long as the gas-phase reaction between
NH₂ and H₂CO is supposed to be efficient. If the correlation
between HNCO and NH₂CHO is confirmed at lower spacial
scales, it is not due to an obvious link with the solid phase.
Finally, even if formamide is easily formed on grains, its return

into the gas phase is often more puzzling than other complex
organic molecules because of its high binding energy and its
very low interaction with water. In summary, the main forma-
tion route of NH₂CHO, by gas-phase or surface reactions, has
not yet been settled and more observational and experimental
work is needed. Another interesting fundamental organic com-
pound in biochemistry studied in this work is the methylamine,
CH₃NH₂, which is known to be the most abundant amine-
containing molecule after formamide (NH₂CHO). Methylamine
has been detected in the gas phase through its 2₀₂⁻ > 1₁₀Aₐ⁻-
state transition in the direction of Sgr B2 and Ori A (Fourikis
et al. 1974) towards the giant molecular cloud Sgr B2(N) with
a fractional abundance as high as 3 × 10⁻⁷ relative to molecu-
lar hydrogen (Nummelin et al. 2000). It has also been detected in
the coma of comet 67P/Churyumov-Gerasimenko (Altwegg et al.
2016) by the Rosetta space mission. In the gas phase, the forma-
tion of the methylamine molecules is completely dependent on
radicals CH₃• and NH₂• produced by UV photons (Garrod et al.
2008). In the solid phase, the hydrogenation experiments of HCN
molecules by H atoms at low surface temperature (Theule et al.
2011) have shown the formation of the fully saturated species
CH₃NH₂ with methanimine as an intermediate. The desorption
of these molecules occurred between 140 and 150 K, at slightly
lower temperatures than the desorption of the amorphous water
ice in their experimental conditions. Recent thermal desorption
experiments of Souda (2016) have shown that methylamine-
water interaction is influenced by the porosity of the ASW ice.
An efficient incorporation of CH₃NH₂ molecules in the porous
water ice film, deposited on Nickel Ni(111) substrate at 20 K
has been observed, with a narrow desorption peak at 160 K,
during water ice crystallization. In contrast, no diffusion of
CH₃NH₂ molecules in the film interior of the non-porous water
ice, deposited at surface temperature 120 K, has been observed
in its TPD spectra, even by hydrogen bonding formation with
H₂O molecules. Despite this advanced work, no experimental
values for the desorption energies of methylamine have been pro-
vided on water ice. However, a desorption energy value (6584 K)
of CH₃NH₂ is given in http://kidaobs.u-bordeaux1.fr/
species/154/CH3NH2.html from a previous estimation of the
OSU gas-grain code of Eric Herbst's group. Within molecu-
lar clouds, the desorption of molecules from icy mantles back
into the gas-phase occurs either by thermal, or non-thermal pro-
cesses. Non-thermal desorption of molecules may result from
the exothermic reactions occurring on the grain surface (Duley
& Williams 1993; Vasyunin & Herbst 2013; Dulieu et al. 2013;
Minissale et al. 2016) and the impact of cosmic rays or ultra-
violet photons (Leger et al. 1985; Hartquist & Williams 1990).
Thermal desorption process occurs during the collapse of the
dense clouds and the birth of protostars (Garrod et al. 2007). The
gravitational energy is converted into radiation, provoking the
warm-up of the grain and the desorption of molecules from the
icy mantle to the gas environment. In laboratory, temperature-
programmed desorption (TPD) is the most effective method for
the measurement of ice sublimations over a significantly shorter
timescale and for the determination of the energy required for
desorption.

In this work, we investigate thermal desorption experiments
of formamide (NH₂CHO) and methylamine (CH₃NH₂) adsor-
bate in the sub-monolayer and monolayer regimes on two sur-
faces. These surfaces are that of the highly orientated pyrolytic
graphite (HOPG) as a laboratory model for carbonaceous grains
and the surface of the H₂O non-porous amorphous solid water
(np-ASW) ice, covering the HOPG substrate and acting as an
extremely relevant astrophysical surface analogue. The aim of
this work is to understand the interaction of these two amino
molecules with the water ice and to study the effect of the
graphitic substrate on the desorption processes. For this purpose,
we determine the desorption energy distributions of formamide
and methylamine on both surfaces, using TPD measurements
and Polanyi–Wigner equation. We compare these distributions
to the binding energy of pure water ice. This paper is orga-
nized as follows: Sect. 2 explains the experimental methods,
Sect. 3 presents the experimental results and the TPD measure-
ments of formamide (NH₂CHO) and methylamine (CH₃NH₂) on
graphite (HOPG) and on np-ASW ice surfaces, Sect. 4 describes
the model developed to measure the desorption energy distribu-
tions of formamide and methylamine molecules from graphite
and water ice surfaces, Sect. 5 presents the discussion of the
results, and finally Sect. 6 summarizes the main conclusions of
this work.

**2. Experimental methods**

The experiments were performed using the FORMOLISM (FORMation of MOLEcules in the InterStellar Medium) apparatus. The set-up is dedicated to study the interaction of atoms and molecules on surfaces of astrophysical interest. The experimental set-up is briefly described here and more details are given in earlier papers (Amiaud et al. 2007; Chaabouni et al. 2012). The apparatus is composed of an ultra-high vacuum (UHV) stainless steel chamber with a base pressure 10<sup>-10</sup> mbar. The sample holder is located in the centre of the main chamber. It is thermally connected to a cold finger of a closed-cycle He cryostat. The temperature of the sample is measured in the range 40–350 K by a calibrated platinum (Pt) diode clamped to the sample holder, which is made of 1 cm diameter copper block, covered with a highly orientated pyrolytic graphite (HOPG, ZYA-grade) slab.

In our laboratory experiments, the viscous, liquid formamide
is introduced in a pyrex flask, which is placed in a ceramic bath
containing a silicone oil acting as a regulator for the tempera-
ture. Because of the low source vapour pressure of formamide
in the beam line at room temperature, the liquid is warmed up to
50 °C using a heating plate with a motor speed of 280 revolutions
per minute. Methylamine compound is also used under its aque-
ous solution with a weight percent in water of 40 wt%, meaning
that there is 40 g of NH₂CH₃ solute for every 100 g of water
solvent. Methylamine is more volatile than formamide and its
source pressure at the inlet of the beam line is set to 1.00 mbar at
room temperature. At these experimental conditions, formamide
and methylamine beams were aimed at the surface of the HOPG
substrate, held at 40 K, for several deposition times, using a triply
differentially pumped beam line, orientated 60° with respect to
the surface of the sample holder.

The UHV chamber is also equipped with a movable
quadrupole mass spectrometer (Hiden Analytical QMS) operat-
ing in the range 1–100 amu (atomic mass unit) with a Channel-
tron detector. The QMS is orientated face-on to the beam line
to characterize the gas composition of formamide and methy-
lamine beams. It is placed 5 mm in front of the surface of the
sample holder to apply the TPD technique using a custom Lab-
View software that maintains a linear heating rate of 0.2 K s⁻¹.
During the warm-up phase of the sample, from 40 to 240 K, the
species desorbing from the surface into the gas phase are ion-
ized, or fragmented into cracking patterns, by electron impact
in the ion source of the QMS. The TPD curves shown in next
sections exhibit the most intensive signals monitoring with the

QMS of the intact parent molecules NH₂CHO (m/z = 45 amu), NH₂CH₃ (m/z = 31 amu), and H₂O (m/z = 18 amu), which are only converted into positive ions by electron impact ionization. The QMS is also moved to the upper position to prepare the films of the non-porous amorphous solid water (np-ASW) ice on the graphite surface, using a micro-channel array doser (1 cm in diameter), located 2 cm in front of the surface in the UHV chamber. The np-ASW ice film of 10 ML thickness is grown on top of the graphite (HOPG) surface, maintained at the temperature of 110 K, by spraying water vapour under a constant deposition pressure in the vacuum chamber of 2 × 10⁻⁹ mbar. Water vapour is obtained from deionized liquid H₂O, purified by several pumping cycles under cryogenic vacuum conditions (Noble et al. 2012). After deposition, the temperature of the surface is kept constant at 110 K for 30 min, until the background pressure in the vacuum chamber is stabilized at 10⁻¹⁰ mbar. Then the sample was cooled to the base temperature 40 K prior to formamide or methylamine deposition. During the cooling of the water ice from 110 to 40 K, the structure and the morphology of the water ice is not changed. Water ice deposited at 110 K remains in the same compact (non-porous) amorphous state at 40 K.

Since our desorption experiments are performed in the sub-
monolayer and monolayer regimes, the dimensionless surface
coverage (θ = N/N<sub>mono</sub> ≤ 1) is defined as the number density of
molecules exposed on the surface (N) by the maximum surface
number density of molecules N<sub>mono</sub> prior to multi-layer desorp-
tion (Noble et al. 2012). At surface coverage saturation (θ = 1),
the first monolayer of molecules covering the surface is defined
as the maximum number density of molecules that populate 10<sup>15</sup>
adsorption site per cm<sup>2</sup> on a flat surface, such as graphite. This
definition of one monolayer unit (1 ML = 10<sup>15</sup> molecules cm<sup>-2</sup>)
is kept over this study; this includes amorphous surfaces, such
as non-porous ASW ice, where the saturation of the first layer
of molecules can thus be observed at a value, which differs
from the exact value of the defined 1 ML. In our experiments,
the first monolayer of solid formamide covering the surface of
graphite at 40 K was reached after 90 min of exposure time,
and that of solid methylamine after beam deposition during
10 min. The fluxes of formamide and methylamine molecules
coming from the gas phase and hitting the surface of the sam-
ple holder are defined as the ratio of the amount of molecules
in the designed 1 ML divided by the exposure time required
for surface saturation. These fluxes derived from TPD data
and the method described in Noble et al. (2012) are estimated
to be 2.6 × 10<sup>10</sup> molecules cm<sup>-2</sup> s<sup>-1</sup> for NH<sub>2</sub>CHO beam and
1.6 × 10<sup>12</sup> molecules cm<sup>-2</sup> s<sup>-1</sup> for CH<sub>3</sub>NH<sub>2</sub> beam.

**3. Experimental results**

3.1. Formamide

3.1.1. Formamide on graphite surface

Figure 1 shows the desorption curves of formamide (NH₂CHO) given by the QMS signals of *m/z* = 45, for several exposure doses (0.15, 0.30, 0.61, and 1.00 ML) on the graphite HOPG surface. The fifth TPD spectrum corresponds to the multi-layer regime of formamide given by the higher exposure dose of 1.66 ML. All the TPD spectra exhibit desorption peaks between 160 and 200 K. Although the integrated area under the TPD curves increases with the exposure dose of formamide from 0.15 to 1.66 ML, the desorption peak remains at the same temperature of 176 K, mainly for surface coverage higher than 0.30 ML. For the lowest dose of 0.15 ML, the TPD peak is shifted to a slightly
<figure><img src="image_1.png" /><figcaption>**Fig. 1.** Desorption rates of formamide (NH₂CHO; *m/z* = 45), expressed (ML s⁻¹) as a function of the temperature of the surface for several exposure doses (0.15, 0.30, 0.61, 1.00, and 1.66 ML) of solid formamide on the cold HOPG surface at 40 K. The linear heating rate of the samples is 0.2 K s⁻¹. The linear dependence of the integrated area under the TPD curves as a function of the exposure time is shown in the inset.</figcaption></figure>

higher temperature compared to the higher doses. The inset in Fig. 1 shows the linear evolution of the integrated areas under the TPD curves (for surface dose up to 1 ML and above) as a function of the exposure times.

### 3.1.2. Formamide on np-ASW ice

Figure 2 shows the desorption curve of solid NH₂CHO (*m/z* = 45) on np-ASW ice, peaking at 176 K. For comparison, the desorption curve of the non-porous ASW ice film, given by the signal (*m/z* = 18) at 150 K, is also shown. Formamide is clearly desorbing from the surface at a higher temperature than the water ice. The TPD curve of formamide from the water ice surface is similar to that obtained previously from the graphite HOPG surface for the same exposure dose of 1 ML. This means that the desorption of formamide molecules into the gas phase is not affected by the water ice substrate. The calculations of the integrated areas below the TPD curves show that more than 0.95 ML of solid formamide is likely to diffuse from the surface of the water ice towards the graphite HOPG substrate. This diffusion probably occurs during the warm-up phase of the sample and the reorganization of the water ice. Since our TPD experiments last few minutes, the diffusion timescale of the molecules from the surface of the water ice to the graphitic substrate is expected to be about few seconds. Because formamide desorbs after water, its binding energy from the HOPG surface is expected to be higher than that of H₂O molecules.

### 3.2. Methylamine

Similarly to formamide, the adsorption-desorption experiments of methylamine CH₃NH₂ molecules were investigated both on graphite (HOPG) and on np-ASW ice surfaces.

#### 3.2.1. Methylamine on graphite surface

Figure 3 shows the desorption curves of methylamine (*m/z* = 31) for several exposure doses (ML) on graphite surface held at 40 K. For very small doses (0.18, 0.26 ML), molecules occupy the most energetically favourable adsorption sites and are tightly bound to the surface of the HOPG, desorbing late from the surface, at temperatures up to 160 K. This small TPD peak is assigned to the

<figure><img src="image_2.png" /><figcaption>**Fig. 2.** TPD curves of formamide (NH₂CHO) giving the desorption rates (ML s⁻¹) of the mass (*m/z* = 45) as a function of the temperature of the surface (K). The red line indicates the TPD signal of NH₂CHO deposited on graphite (HOPG) surface at 40 K; the black dashed line shows the TPD signal of NH₂CHO deposited on the np-ASW ice surface at 40 K; and the blue dashed line indicates the TPD signal of H₂O (*m/z* = 18) for 10 ML thickness of the np-ASW ice film prepared at 110 K on the HOPG surface and cooled down to 40 K (scaled by 0.0007).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 3.** Desorption rates, expressed (ML s⁻¹), of methylamine (CH₃NH₂) as a function of the temperature of the surface (K) for several exposure doses of solid methylamine (0.18, 0.26, 0.46, 0.70, 0.80, 1.0, and 1.40 ML) on the cold HOPG surface at 40 K. The linear heating rate of the samples is 0.2 K s⁻¹.</figcaption></figure>

strong interaction of the NH₂CH₃ molecules with the graphitic surface in the sub-monolayer regime. As the surface coverage increases, molecules are forced to populate progressively less tightly bound sites of the graphitic HOPG surface, provoking earlier desorption at about 113 K. The area of the second desorption peak of CH₃NH₂ at 113 K increases with the increase of the exposure doses in the sub-monolayer regime, and its maximum shifts towards a lower temperature (106 K) once the surface coverage is saturated and the first monolayer is formed. The strong desorption peak at 106 K for 1.40 ML corresponds to the onset of the multi-layer desorption of solid methylamine, where CH₃NH₂ is bound to CH₃NH₂ ice by hydrogen bonds.

#### 3.2.2. Methylamine on np-ASW ice

Figure 4 shows the TPD curves of solid methylamine (*m/z* = 31) from the np-ASW ice surface for two small doses (0.30 and
0.35 ML) deposited on the surface during 5 and 6 min, respectively (thick red and magenta lines). These curves are compared to the TPD curve of solid methylamine on the graphite (HOPG) surface for a 1 ML exposure dose (thin red line) and to the H₂O TPD curve (m/z = 18) of pure np-ASW ice, with 10 ML thickness, grown on the HOPG surface at 110 K (blue dashed line). As shown in Fig. 4, the large TPD peak of solid CH₃NH₂ (1 ML) from the HOPG surface shows a multi-layer desorption peak at lower surface temperatures centred at 106 K, a shoulder at about 140–150 K resulting from the mixture of the methylamine with the water coming from the aqueous phase, and a long desorption tail at higher temperatures, up to 220 K. When CH₃NH₂ is deposited on top of the np-ASW ice film of 10 ML thickness, prepared at 110 K and cooled down to 40 K, the maximum of the desorption peak of methylamine is shifted to the higher temperature, 137 K, and a large desorption peak with a maximum centred at 160 K appears as a tail at higher surface temperatures up to 220 K. This desorption behaviour of methylamine on the np-ASW ice is observed for two close exposure doses of 0.30 and 0.35 ML. The desorption peaks at 137 K, which occur before the desorption of pure water ice at 150 K, and even the crystallization phase of H₂O at about 145 K, correspond to CH₃NH₂ molecules desorbing from the surface of the water ice. Our experimental results show that, when increasing slightly the exposure dose of methylamine on the np-ASW ice surface from 0.30 to 0.35 ML, the fraction of CH₃NH₂ ice desorbing from the water ice surface at 137 K increases from 0.16 to 0.21 ML, while those desorbing directly from the HOPG surface at T ≥ 160 K decreases slightly from 0.16 to 0.14 ML, respectively. This means that by increasing the amount of methylamine on top of the water ice surface, CH₃NH₂ molecules bind further with the water ice by hydrogen bonds and desorb between 120 and 140 K, rather than diffuse through the water ice surface and desorb later from the HOPG substrate at 160–220 K. The fraction of the refractory CH₃NH₂ molecules desorbing from the HOPG substrate after water ice sublimation is about 0.15 ML.

Our results are partially in agreement with those of Souda (2016), who observed a broad TPD curve of methylamine from the np-ASW ice of D₂O (8 ML), deposited at 120 K on the nickel Ni(111) substrate. This latter comprises two desorption peaks: one peak at 120 K corresponding to multilayer desorption of methylamine and another at about 150 K corresponding to methylamine mixed with water coming from the aqueous solution. In addition, the TPD spectrum of Souda (2016) shows no desorption peak of methylamine at surface temperature 160 K and above, suggesting that, in contrast to our case, no strong interaction between methylamine and the underlying Ni(111) substrate takes place in their experiments. If our experiments performed on the np-ASW ice of 10 ML thickness allowed the incorporation of methylamine from the water ice surface towards the graphite substrate, one can conclude that the diffusion of methylamine molecules through the non-porous water ice surface depends on the substrate below the water ice (HOPG, Ni). The nickel Ni(111) surface is expected to have fewer energetic binding sites than HOPG surface. However, if differences of substrates are seen for methylamine, one could say that similar differences are expected for formamide. The role of the substrate is discussed later.

## 4. Analysis

A simple mathematic model has been developed to fit the TPD curves of formamide and methylamine in the sub-monolayer and monolayer regimes. At any surface coverage, thermal desorption

<figure><img src="image_4.png" /><figcaption>Fig. 4. TPD curves of methylamine giving the desorption rates (ML s⁻¹) of the mass (m/z = 31) as a function of the temperature of the surface (K). The thin red line indicates 1 ML of CH₃NH₂ deposited on graphite HOPG substrate at 40 K; the thick red line represents 0.30 ML of CH₃NH₂ deposited on the np-ASW ice surface held at 40 K; the thick magenta line indicates 0.35 ML of CH₃NH₂ deposited on the np-ASW ice surface at 40 K; and the blue dashed line represents TPD curve of H₂O (m/z = 18) for 10 ML of the np-ASW ice film prepared at 110 K on the HOPG surface and cooled down to 40 K (scaled by 0.001).</figcaption></figure>

of molecules from the surface into the gas phase can be described in terms of an Arrhenius law, given by the Polanyi–Wigner Eq. (1) (Noble et al. 2012; Dohnálek et al. 2001)

$$r(T) = -\frac{dN}{dt} = AN^a e^{-E_{\text{des}}/k_B T}, \quad (1)$$

where r(T) is the desorption rate (molecule cm⁻² s⁻¹), N is the number density of molecules adsorbed on the surface, expressed (molecules cm⁻²), a is the order of the desorption process, A is the pre-exponential factor expressed (molecule⁻¹ cm²a⁻² s⁻¹), which can be considered to be the attempt frequency of molecules at overcoming the barrier to desorption, k_B is the Boltzmann constant (k_B = 1.38 × 10⁻²³ J K⁻¹), t is the time (s), T is the absolute temperature of the surface (K), and E_des is the activation energy for desorption (kJ mol⁻¹) or (K), where 1 kJ mol⁻¹ = 120 K.

In the particular case of simple molecular adsorption, the pre-exponential factor A may also be equated with the frequency of vibration of the bond between the molecule and substrate; this is because every time this bond is stretched during the course of a vibrational cycle can be considered an attempt to break the bond and hence an attempt at desorption. However, we point out that this is a simplistic view of a complex problem. The physical observable parameter is the desorption flux; the pre-exponential factor and the binding energy are actually two degenerated parameters linked in the Polanyi–Wigner equation. Therefore, at anytime, a couple of solutions (A, E_des) should be considered.

Because the peaks of the TPD curves of formamide appear at a single temperature value for all the exposure doses up to 1.61 ML, the desorption of formamide is considered to be of first order, and the desorption energy is expected to be dependent on the coverage (Fraser et al. 2001).

For TPD of first order, a = 1, the desorption rate r(T) become

$$r(T) = -\frac{dN}{dt} = ANe^{-E_{\text{des}}/k_B T}, \quad (2)$$
where the pre-exponential factor A for desorption (s⁻¹).

The desorption rate r(T) (ML s⁻¹) can be expressed using Eq. (3)

$$r(T)_{\text{ML s}^{-1}} = \frac{r(T)}{\beta^{-1} \left( \int_{T_{\text{min}}}^{T_{\text{max}}} \frac{dN}{dt} \cdot dT \right)}, \quad (3)$$

where $\left(\int_{T_{\text{min}}}^{T_{\text{max}}} \frac{dN}{dt} \cdot dT\right)$ is the integrated area below the TPD curve of the designed 1 ML exposure dose between $T_{\text{min}}$ and $T_{\text{max}}$.

In this model, we consider that each exposure dose N (ML) of molecules on the surface is the sum of the different fraction exposure doses $N_i$ (ML),

$$N = \sum_{i=1}^{n} N_i = N_1 + N_2 + \dots, \quad (4)$$

where $N_i$ is the population of molecules desorbing from the surface with a desorption energy $E_i$ at a surface temperature T.

We also assume that the desorption rate r(T) is the sum of the desorption rates $r_i(T)$, i.e.

$$r(T) = \sum_{i=1}^{n} r_i(T) = AN_1e^{-E_1/k_B T} + AN_i e^{-E_i/k_B T} + \dots, \quad (5)$$

where

$$r_i(T) = AN_i e^{-E_i/k_B T} \quad (6)$$

is the desorption rate of the molecular population, $N_i$, desorbing from the surface at a temperature T, with a pre-exponential factor A, and a desorption energy $E_i$.

To fit the TPD data for an exposure dose N of molecules on the surface, we use the desorption rate r(T), given by Eq. (5), then we set two values $E_{\text{min}}$ and $E_{\text{max}}$ for the desorption energy of the molecules from the surface, and we choose a value for the pre-exponential factor A. When we run the program, we obtain the different populations $N_i$ of molecules desorbing from the surface with the desorption energy $E_i$, at a surface temperature T, varying from $T_{\text{min}}$ to $T_{\text{max}}$. The best fit of the TPD data is obtained when the calculated curve matches well the experimental results, and the three computational parameters ($A$, $E_i$, $N_i$) are well constrained, where the pre-exponential factor A is between $10^{12}$ and $10^{18}$ s⁻¹, the desorption energy barrier $E_i$ is between $E_{\text{min}}$ and $E_{\text{max}}$, and all the surface populations $N_i$ satisfy the relation (4).

## 4.1. Desorption energies of formamide

The top panel of Fig. 5 shows the best fits of the TPD curves of formamide for various surface doses (0.14, 0.30, 0.61 and 1.0 ML) on the graphite (HOPG) surface. These best fits are derived from Eq. (5) with a pre-exponential factor $A = 10^{18}$ s⁻¹. The use of a low pre-exponential factor ($A = 10^{12}$ s⁻¹) in our modelling simulations does not reproduce the TPD curves on the graphite surface perfectly. The bottom panel of Fig. 5 shows the surface population $N_i$ of formamide molecules (ML) as a function of the desorption energy $E_i$ (K) on the graphite (HOPG) surface for the first monolayer exposure coverage ($N = 1$ ML). As shown in Fig. 5, bottom panel, most of the surface population ($\sum_{i=1}^n N_i = 0.97$ ML) of formamide on HOPG surface releases into the gas phase with a desorption energy distribution, ranging from 7460 to 9380 K.

The same desorption energy distribution (7460–9380 K) is obtained by fitting the TPD data of formamide deposited on top of the np-ASW ice film of 10 ML thickness, covering the graphitic HOPG substrate. This main result is explained by the fast and efficient (>95%) diffusion of NH₂CHO molecules from the water ice surface towards the HOPG substrate, at surface temperature, 40 K, or more probably during the warming-up phase of the ices. The bottom panel of Fig. 5 also shows that for a pre-exponential factor $A = 10^{18}$ s⁻¹, the maximum of the desorption energy distribution of formamide (7700 K) is higher than that of pure amorphous water ice ($E_{\text{des}} = 6490$ K), calculated with the same pre-exponential value $A = 10^{18}$ s⁻¹ from the parameters ($E_{\text{des}}$, A) of the amorphous water ice (Fraser et al. 2001). This means that NH₂CHO molecules are more tightly physisorbed to the surface of the HOPG substrate than H₂O molecules.

## 4.2. Desorption energies of methylamine

Similar calculations of the desorption energy distribution of methylamine have been carried out both on graphite HOPG and np-ASW ice surfaces. Assuming a first order desorption process of methylamine on graphite surface, the best fits of the TPD curves for various values of the surface exposure coverage, N (0.25, 0.46, 0.71, and 1.0 ML) of methylamine, obtained from the model with the pre-exponential factor $A = 10^{12}$ s⁻¹, are shown in Fig. 6.

The top panel of Fig. 7 shows the surface population $N_i$ (ML) of solid methylamine on graphite (HOPG) surface as a function of the desorption energy $E_i$ of methylamine (K), for the first monolayer exposure coverage ($N = 1$ ML). The desorption energy distribution of methylamine from graphite is found to range between 3010 and 8420 K, where a large percentage (~0.80 ML) of molecules desorbing with low binding energies (3010–4454 K) correspond to the multi-layer and monolayer desorptions of CH₃NH₂ species from the graphite surface. The range of the desorption energy (5050–8420 K) is assigned to the surface population (~0.15 ML) of methylamine that desorbs from the very energetic adsorption sites of the graphite (HOPG) surface.

In the case of Fig. 7, bottom panel, where an exposure dose $N = 0.30$ ML of solid methylamine is deposited on top of the np-ASW ice film, the desorption energy distribution of these molecules is reduced to the range (3900–8420 K), with traces of small energies (2770–3610 K) corresponding to methylamine multi-layer desorption. The bottom panel of Fig. 7 also shows that a surface population of about 0.15 ML of CH₃NH₂ leaves the water ice surface with desorption energies (3900–4500 K), which is lower than the binding energy value (4930 K) of crystalline water ice, calculated with the same pre-exponential factor $A = 10^{12}$ s⁻¹ from the desorption parameters ($E_{\text{des}}$, A) of Fraser et al. (2001). Furthermore, the desorption energies (5050–8420 K), which are higher than those of the amorphous water ice, are attributed to the fraction ($\sum_{i=1}^n N_i = 0.15$ ML) of methylamine population that diffuses through the water ice surface towards the highest binding sites of the HOPG substrate, and then desorbs into the gas phase after water ice sublimation.

# 5. Discussion

We developed a model using the Polanyi–Wigner equation to reproduce the TPD profiles and determine the desorption energy distributions of NH₂CHO and CH₃NH₂ molecules on graphite
<figure><img src="image_5.png" /><figcaption>**Fig. 5.** Modelling results of the desorption rates (ML s⁻¹) and the desorption energy distribution (K) of formamide on graphite (HOPG) surface. Top panel: red crosses indicate TPD data of NH₂CHO (m/z = 45) on HOPG surface for different exposure doses of 0.14, 0.30, 0.61, and 1.0 ML; blue lines: the best fits of the TPD curves of NH₂CHO from the HOPG surface, calculated with the pre-exponential factor A = 10¹⁸ s⁻¹ are shown. Bottom panel: the surface population (ML) of NH₂CHO on HOPG surface as a function of the desorption energy (K) is shown. The desorption energy distribution (Eᵢ) and the surface population (Nᵢ) of formamide are derived from Eq. (5) with the best pre-exponential factor A = 10¹⁸ s⁻¹ for the exposure dose N = Σᵢ=¹ Nᵢ = 1 ML.</figcaption></figure>

(HOPG) and non-porous ASW ice surfaces in the sub-monolayer and monolayer regimes. The desorption energy distributions, E<sub>des,dist</sub>, of formamide and methylamine are obtained with different pre-exponential factors: A = 10<sup>18</sup> s<sup>-1</sup> for formamide and A = 10<sup>12</sup> s<sup>-1</sup> for methylamine. In the case of formamide (NH<sub>2</sub>CHO), the decrease in the pre-exponential factor A from 10<sup>18</sup> to 10<sup>12</sup> s<sup>-1</sup>, affects the quality of the TPD fits, and reduces the value of the desorption energy of the molecules by 30%. As

already mentioned, A and E<sub>des</sub> are degenerated parameters that
can be derived from a desorption flux at a given temperature
T. However, the dynamic of desorption gives more constraints
on the couple of parameters. Experimentalists seeks for getting
the best fit from their experiments, and as evidence, the best
fit is obtained with extreme differences in the pre-exponential
factor values (A = 10<sup>18</sup> and A = 10<sup>12</sup> s<sup>-1</sup>) for two apparently
similar molecules. The degeneracy of A and E<sub>des</sub> has been
<figure><img src="image_6.png" /><figcaption>Fig. 6. Modelling results of the desorption rates (ML s⁻¹) of methylamine on graphite (HOPG) surface. Red crosses: TPD data of CH₃NH₂ (m/z = 31) on HOPG surface for different exposure doses of 0.25, 0.46, 0.71, and 1.0 ML are shown; blue lines: the best fits of the TPD curves of CH₃NH₂ from the HOPG surface, calculated with the best pre-exponential factor A = 10¹² s⁻¹ are represented.</figcaption></figure>

already estimated and discussed previously. Simple molecules (like H₂) seems to have a pre-exponential factor for desorption usually close to 10¹²⁻¹³ s⁻¹ (Amiaud et al. 2006). On the contrary, Doronin et al. (2015) have shown that the same molecule (CH₃OH) could have different pre-exponential factors for different substrates or regimes (multi-layers or sub-monolayer). These authors proposed a method to derive the pre-exponential factor from TPD data. It has been suggested by Tait et al. (2005) that the pre-exponential factor A for the desorption depends on the potential interaction of the adsorbate substrate system, and the number of degrees of freedom of the molecule when it passes from the adsorbate state to the gas-phase transition state. These authors have demonstrated the increase of the pre-factor A for desorption with the chain length of the molecule from the value 10¹³ to 10¹⁹ s⁻¹, and have explained this variation of A by the increase in the rotational entropy available to the molecules in the gas-like transition state for desorption. The difference in the pre-exponential factor values is an experimental fact. In this work, we want to determine the binding energy distributions of molecules, and once done, we need to be able to compare the different values, originating from different works or analysis methods.

Table 1 shows the maximum of the desorption energies (E<sub>des,max</sub>) of formamide and methylamine from different substrates, calculated from the model, with the original suitable pre-exponential factors (A), and with a fixed value (A = 10¹² s⁻¹) for better comparison with other relevant astrophysical molecules, using the following desorbing flux relationship:

$$r(T) = A_1 e^{-E_{1,\text{des}}/k_B T} = A_2 e^{-E_{2,\text{des}}/k_B T}, \quad (7)$$

where A₁ and A₂ are the pre-exponential factors (s⁻¹), associated with the desorption energies E₁,des and E₂,des, respectively, of the adsorbed molecules on the surface, and T is the experimental temperature (K) of the surface, at which the desorption is observed.

In Table 1, we can compare the value of the binding energy of methanol (CH₃OH) on graphite with those of methylamine and formamide. We can see that even though the pre-exponential factors and analysis methods are different, all the approximated values of binding energies given here are close and can be compared to the value of the binding energy of the amorphous water ice derived from the same calculation method. The important result here is that, in any case, the binding energy of CH₃OH is lower than that of water. Table 1 also shows that for the same employed pre-exponential factor A = 10¹² s⁻¹, the maximum of the desorption energy distribution (E<sub>des,max</sub> = 5265 K) of NH₂CHO from graphite (HOPG) substrate is smaller than the value (6871 K) of the mean desorption energy obtained from silicate (SiO₂) interstellar grain analogue surface by Dawley et al. (2014). This difference between our result and that of Dawley et al. (2014) is an indication that the desorption energy of formamide depends on the substrate itself.

More precisely, we find that the binding energy of 0.1 ML of formamide adsorbed on graphite substrate is 5600–5900 K, calculated with A = 10¹² s⁻¹. These values are smaller than the value given on silicate substrate (Dawley et al. 2014). This difference may not be only related to the composition of the substrate (silicate, graphite), but could also be due to the difference in the morphology of the substrate, which can easily change the
<figure><img src="image_7.png" /><figcaption>**Fig. 7.** Modelling results of the desorption energy distributions (K) of methylamine on graphite (HOPG) and np-ASW ice surfaces. *Top panel:* surface population (ML) of CH<sub>3</sub>NH<sub>2</sub> (m/z = 31) as a function of the desorption energy (K) for an exposure dose *N* = 1 ML of CH<sub>3</sub>NH<sub>2</sub> on the HOPG surface. *Bottom panel:* surface population (ML) of NH<sub>2</sub>CH<sub>3</sub> as a function of the desorption energy (K) for an exposure dose *N* = 0.30 ML of CH<sub>3</sub>NH<sub>2</sub> on the surface of the np-ASW ice film of 10 ML thickness, prepared at 110 K and cooled down to 40 K. The desorption energy distribution (*E*<sub>i</sub>) and the surface population (*N*<sub>i</sub>) of methylamine are derived from Eq. (5) with the best pre-exponential factor *A* = 10<sup>12</sup> s<sup>-1</sup> for the two exposure doses *N* = Σ<sup>n</sup><sub>i=1</sub> *N*<sub>i</sub> = 1 ML on HOPG and *N* = Σ<sup>n</sup><sub>i=1</sub> *N*<sub>i</sub> = 0.30 ML on np-ASW ice surfaces.</figcaption></figure>

binding energy distribution of the molecules by a few tens of
percent (Fillion et al. 2009). In our experiments, the desorption
energy of formamide from the surface of the non-porous ASW
ice cannot be measured because the water substrate desorbs
before formamide, that is deposited on top of it. Actually, the
whole binding energy distribution of formamide from graphite
(5056–6990 K), calculated with A = 10¹² s⁻¹ for 1 ML cover-
age, is higher than the binding energy values of water ice in its
amorphous (4810 K), and crystalline state (4930 K). Unlike for-
mamide, solid methylamine can desorb under different forms, in
the multi-layer regime (NH₂CH₃–NH₂CH₃) with low desorption
energies (3010–3490 K) from the np-ASW ice surface with des-
orption energies (3900–4500 K) and even later from the HOPG
substrate with higher desorption energies (5050–8420 K). The
different desorption energies of methylamine calculated in this
work with respect to that of pure amorphous water ice (4810 K)
is due to its wetting ability compared to H₂O molecules. In fact,
CH₃NH₂ species are able to spread readily and uniformly over

the surface of the graphite (HOPG) or the amorphous water ice
by hydrogen bonds, thereby forming a thin and continuous film
in which physisorbed molecules populate a large distribution of
surface binding sites. The proportion of molecules desorbing,
prior, during, or after the water ice varies with the doses of
methylamine, but each time the fraction of methylamine desorb-
ing after the water ice is about 0.15 ML. However, the fraction
of methylamine co-desorbing with the crystalline phase of the
water ice is very small at about 0.03 ML. We can see in Fig. 4
that the desorption of methylamine is very reduced during the
desorption of the water ice at around 150 K. The desorption of
methylamine at 137 K, before the sublimation of the water ice,
is delayed compared with its desorption without water at T =
106 K (Fig. 4), indicating a stronger interaction of methylamine
with the water molecule than with itself. In most astrophysical
models, the whole desorption of each molecule is described by
its (unique) binding energy. For methylamine, the main ques-
tion is which binding energy shall we propose. Usually, binding
<table><caption>**Table 1.** Desorption energy distributions ($E_{des,dist}$) (K), Col. 3, of NH₂CHO and CH₃NH₂ obtained in this work with the best-fit pre-exponential factor A values, expressed (s⁻¹).</caption><thead><tr><th rowspan="2">Molecule</th><th rowspan="2">Substrate</th><th>E<sub>des,dist</sub> (A)</th><th>E<sub>des,max</sub> (A)</th><th>E<sub>des,max</sub><br>(A = 10<sup>12</sup> s<sup>-1</sup>)</th><th rowspan="2">References</th></tr><tr><th>K (s<sup>-1</sup>)</th><th>K (s<sup>-1</sup>)</th><th>K</th></tr></thead><tbody><tr><td>NH<sub>2</sub>CHO</td><td>HOPG</td><td>7460–9380 (10<sup>18</sup>)</td><td>7700 (10<sup>18</sup>)</td><td>5265<br>E<sub>des,dist</sub> = 5056–6990</td><td>This work</td></tr><tr><td>NH<sub>2</sub>CHO</td><td>H<sub>2</sub>O</td><td></td><td></td><td></td><td>This work</td></tr><tr><td>NH<sub>2</sub>CHO</td><td>SiO<sub>2</sub></td><td></td><td>7397 (10<sup>13</sup>)</td><td>6871</td><td>Dawley et al. (2014)</td></tr><tr><td>CH<sub>3</sub>NH<sub>2</sub></td><td>NH<sub>2</sub>CH<sub>3</sub></td><td>3010–3490 (10<sup>12</sup>)</td><td>3307 (10<sup>12</sup>)</td><td>3307</td><td>This work</td></tr><tr><td>CH<sub>3</sub>NH<sub>2</sub></td><td>H<sub>2</sub>O</td><td>3900–4500 (10<sup>12</sup>)</td><td>4269 (10<sup>12</sup>)</td><td>4269</td><td>This work</td></tr><tr><td>CH<sub>3</sub>NH<sub>2</sub></td><td>HOPG</td><td>5050–8420 (10<sup>12</sup>)</td><td>5100 (10<sup>12</sup>)</td><td>5100</td><td>This work</td></tr><tr><td>NH<sub>2</sub>OH</td><td>Silicate</td><td></td><td>6518 (10<sup>13</sup>)</td><td>6080</td><td>Congiu et al. (2012)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>CH<sub>3</sub>OH</td><td></td><td>4989 (5 × 10<sup>14</sup>)</td><td>4169</td><td>Doronin et al. (2015)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>H<sub>2</sub>O</td><td></td><td>4366 (2 × 10<sup>12</sup>)</td><td>4310</td><td>Martín-Doménech et al. (2014)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>Graphite</td><td></td><td>5454 (10<sup>16</sup>)</td><td>4257</td><td>Doronin et al. (2015)</td></tr><tr><td>H<sub>2</sub>CO</td><td>H<sub>2</sub>O</td><td></td><td>3247 (10<sup>13</sup>)</td><td>2899</td><td>Noble et al. (2012)</td></tr><tr><td>H<sub>2</sub>CO</td><td>Silicate</td><td></td><td>3729 (10<sup>13</sup>)</td><td>3040</td><td>Noble et al. (2012)</td></tr><tr><td>H<sub>2</sub>O</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Amorphous</td><td>Au</td><td></td><td>5600 (10<sup>15</sup>)</td><td>4810</td><td>Fraser et al. (2001)</td></tr><tr><td>Crystalline</td><td>Au</td><td></td><td>5773 (10<sup>15</sup>)</td><td>4930</td><td>Fraser et al. (2001)</td></tr></tbody></table>

**Notes.** Col. 4 gives the maximum of the desorption energy ($E_{des,max}$) (K) obtained with the best-fit pre-exponential factor A values (s⁻¹) for NH₂CHO, NH₂CH₃, and other astrophysical relevant molecules (NH₂OH, CH₃OH, H₂CO, and H₂O) taken from the literature. For a comparison, Col. 5 gives the desorption energies ($E_{des,max}$) of all the molecules calculated with the typical pre-exponential factor A = 10¹² s⁻¹ for various grain surfaces, using Eq. (7) of flux desorption ($A_1e^{-E_{1,des}/k_BT} = A_2e^{-E_{2,des}/k_BT}$), and the values of A and $E_{des,max}$ in Col. 4.

energies are measured for pure species and therefore, the answer would be $E_{des} \approx 3000$ K with $A = 10^{12}$ s⁻¹. But in an astrophysical context, the proportion of methylamine in icy mantles is certainly less than a few % as it is not positively detected in ices (Boogert et al. 2015). Therefore, it would be better to take the low concentration limit of our experiments (~0.15 ML), which would lead to an estimation of the binding energy at around 6000 K, well above the value of those of the water ice. This low coverage value is certainly very dependent on the substrate and represents the wetting properties of the surface for a specific molecule. This is probably why Souda (2016) did not find a late desorption of methylamine in the case of metallic surface Ni(111). The key question is to find out whether at low concentration, the binding energy of a specific molecule is higher than the binding energy of the water ice. Table 1 reveals that the binding energies of methanol (CH₃OH) and formaldehyde (H₂CO) are lower than that of amorphous (H₂O) water ice, and so we can consider these molecules as volatile, or at least they would desorb with the water ice mantle. For some other molecules, such as NH₂OH and NH₂CHO, the binding energy is higher than that of (H₂O) water ice, and we can consider these molecules as refractory species, compared to water molecules. Refractory does not have the same meaning here as sometimes used in shock-regions studies or in geology. Here, it is the remaining part of the molecular mantle after the sublimation of water. Before this study, we were wondering if some simple chemical properties could explain the common trends of the binding energies. It is usually discussed in terms of hydrophilic and hydrophobic proprieties of the molecules or in terms of hydrogen bonding formation with water. We can sort molecules in two groups: those with

a binding energy less than that of water, such as CH₃OH, NH₃, H₂CO, and another group with a binding energy, at low coverage, that are higher than the binding energy of water, among which we can find H₂O₂ (Dulieu et al. 2017), NH₂OH (Congiu et al. 2012), and NH₂CHO. As a matter of fact, the hydrophobic nature of the methyl (–CH₃) group, or the hydrophilic nature of the amino (–NH₂) or hydroxyl (–OH) groups, cannot explain our observations. Only detailed calculations could probably give a real understanding of this empirical sorting.

Formamide and methylamine that diffuse completely or partly through the ASW ice surface towards the graphitic substrate and desorb into the gas phase at higher temperatures (≥160 K) are considered as refractory species, which can remain frozen on dust grains even after water ice sublimation. This result leads us to consider different scenarios, in which formamide and methylamine can be formed either in the gas phase and then accreted onto the ice surface or formed by grain-surface chemistry. In the case of the gas-phase formation, the diffusion of the adsorbed molecules on the colder ice mantle at 10–20 K is an open question, since it depends on the thickness, porosity, and chemical composition of the ice mantle (Mispelaer et al. 2013; Lauck et al. 2015). In the case of grain-surface chemistry, NH₂CHO and CH₃NH₂ molecules may be formed on icy grain mantles in the interstellar medium, by exothermic reactions between mobile radicals, generated by ultraviolet (UV) radiation, or trapped within the bulk of ice mantles of dust grains (Taquet et al. 2012), probably at 30–40 K, once the protostar starts heating its immediate surroundings, as has been suggested by grain surface chemistry models of Garrod & Herbst (2006). The diffusion of the molecules within the water ice
to the surface of dust grains by hydrogen bonding formation
depends on the morphology of the ices (Lauck et al. 2015) and
mainly on the surface of the dust grain below the water ice.
The diffusion of NH₂CHO molecule from the water ice surface
to the graphitic substrate is possibly favoured by the formation
of larger groups of segregated NH₂CHO molecules, which bind
together by intermolecular van der Waals interactions, and with
H₂O molecules by hydrogen bonds through the amino (–NH₂)
and carbonyl (–C=O) functional groups. The fast diffusion of
NH₂CHO molecules through the water ice may occur during
the reorganization of the ices, and the transition phase from
the amorphous to the crystalline structure of the ASW ice at
about 145 K (Mispelaer et al. 2013; Dawley et al. 2014). In
the interstellar medium, dust grains can be composed of rele-
vant astrophysical materials, such as amorphous carbon (a-C),
amorphous silicon (a-Si), and amorphous silicates (Mg₂SiO₄
and Fe₂SiO₄). Amorphous carbon (a-C), such as a diamond, has
been shown to consist of graphitic islands, composed of com-
pact polycyclic aromatic ring structures, poorly connected with
each other Duley et al. (1989). These astrophysical relevant sur-
faces, characterized by deepest binding sites and highest binding
energies, in comparison to the surface of the amorphous water
ices, may affect the diffusion proprieties of the molecules. So
methylamine and formamide molecules interact strongly with
these amorphous carbon and silicon surfaces after water ice
evaporation. Formamide molecules are expected to fully dif-
fuse from the water ice surface to these interstellar analogue
surfaces.

If dust grains are heated, as in the case of those located
nearby a newly born protostar, the external heat provided by the
protostars increases the surface temperature of the ice mantle,
provoking desorption from the ice back to the gas phase of the
volatile molecules, such as CO, CO₂, and H₂O or CH₃OH. As
the thickness of the water ice on the dust grain is reduced, the
non-volatile formamide molecules diffuses through the water ice
and populates the highest bindings sites of dust grains. Therefore
the presence in the gas phase of refractory molecules, if these
molecules come from the solid phase, would require a higher
final temperature of dust grains. These refractory molecules
should be observed on a separate snow line. Furthermore, this
thermal desorption should be accompanied by a blending of
the species and some induced reactivity, as described in for
example Theulé et al. (2013), Dulieu et al. (2017), and in
Souda (2016) for the H-D exchange in ices. But the presence
of molecules in the gas phase coming from the solid phase
can arise from the sputtering of the grain mantle, especially
in shocks (e.g. Draine 1983; Jones et al. 1994; Tielens et al.
1994). This type of desorption process is not at thermal equi-
librium, but is induced by gaseous bombardment with an energy
greater than the surface binding energies, provoking the ejection
of the material in gas environments. This kind of ballistic kick
out mechanism should be sensitive to the binding energy of the
molecules.

Recent astronomical observations of Bacmann et al. (2012)
have suggested that complex organic molecules (COMs) are
actively formed in prestellar cores in L1689B before the grav-
itational collapsing phase leading to protostar formation and
even before the warm-up phase of the grains. Many COMs have
been detected in cold dark prestellar cores at low temperature
(T ~ 10 K). This includes dimethyl ether (CH₃OCH₃),
methyl formate (CH₃OCHO), acetaldehyde (CH₃CHO), ketene
(CH₂CO), cyclopropenone (c-C₃H₂O), propynal (HCCCHO),
vinyl cyanide (CH₂CHCN), and propyne (CH₃CCH) (Jiménez-
Serra et al. 2016; Vastel et al. 2014; Bacmann et al. 2012). Here

one of the main efficient mechanism included in astrochemical
models to feed back the gas phase is the impulsive heating of
dust grains by X-rays and cosmic rays, already proposed ear-
lier by Leger et al. (1985). Here again, the binding energy of
the molecules is still a selective parameter because it explic-
itly enters in the calculation of the desorption of each type of
molecules. Although this is not exactly the same mechanism than
found in thermal desorption, in practice, models sort molecules
depending on their binding energies. Therefore, in the context
of prestellar cores, a very high binding energy also prevents any
return in the gas phase. The second efficient mechanism for pop-
ulating the gas phase is the chemical desorption (or reactive
desorption) (Takahashi & Williams 2000; Garrod et al. 2007;
Dulieu et al. 2013). Here, the energy released during the for-
mation of the molecule itself is the promoter of the desorption.
But the probability of desorption has been proposed to decrease
exponentially with the binding energy, among others factors
(Minissale et al. 2016). The COMs detected in cold dark prestel-
lar cores regions are likely to originate from gas-phase reactions
at 10–20 K of precursor molecules, such as formaldehyde and
methanol, which are previously formed on icy grain surfaces,
then ejected into the gas phase by desorption induced by chem-
ical reaction, and finally followed by gas-phase chemistry via
ion molecules (Vasyunin & Herbst 2013), neutral-neutral, and
radiative association reactions (Vasyunin et al. 2017). These
molecules detectable in the gas phase can in turn be involved
in gas-phase reactions to form more complex organic molecules.
It is therefore, interesting to explore the interaction of these
detected COMs with the ASW ice and with various astrophysical
relevant substrates. Formamide and methylamine are probably
forming in regions where CO has also started to freeze-out, i.e.
in dense molecular clouds. In these regions, the icy mantle might
be composed of water ice in the presence of CO molecules or a
mixture of CO₂ and H₂O ices. However, since CO desorbs at 30–
50 K from the amorphous water ice surface (Noble et al. 2012), it
is probably that its presence with H₂O molecules does not affect
the diffusion of formamide and methylamine from the water ice
surface towards the substrate, such as graphite HOPG, at the
expected temperatures of 110–140 K. Nevertheless, it would be
interesting to perform further adsorption–desorption laboratory
experiments of formamide and methylamine on mixed or lay-
ered CO, CO₂, and H₂O ices to understand the effect of this
relevant astrophysical molecule on the diffusion process of the
complex organic molecules through the ASW ice. It would also
be interesting to explore other substrates, such as amorphous sil-
icon (a-Si) and amorphous carbon (a-C), which better represent
the interstellar dust grains composition than HOPG to study the
effect of the substrate on the desorption energies and the diffu-
sion of these two molecules, and other COMs from the water ice
surfaces.

6. Conclusions

The desorption of formamide NH₂CHO and methylamine
CH₃NH₂ molecules has been investigated experimentally on
graphite (HOPG) and np-ASW water ice surfaces in the sub-
monolayer and monolayer regimes, using the TPD technique.

Experimental results show an efficient diffusion of more
than 95% of formamide through the np-ASW ice film of 10 ML
thickness towards the graphite (HOPG) substrate. The large per-
centage of solid formamide (>0.95 ML) bound to the graphitic
substrate desorbs at higher surface temperature, 176 K, what-
ever the surface coverage, after the desorption of the water ice
at about 150 K. The diffusion of NH₂CHO is likely to occur during the warming-up phase of the ices at a short timescale of few seconds.

CH₃NH₂ molecules physisorbed on the ASW ice desorbs at 137 K, before the desorption of the H₂O molecules at 150 K, and even from the energetic sites of the HOPG surface at higher temperatures 160–220 K. Because of the wetting ability of the methylamine compared to water, the fraction of solid methylamine that diffuses through the water ice surface towards the graphitic substrate is about 0.15 ML. The amounts of formamide and methylamine desorbing from the graphite dust grains after water ice sublimation are considered as refractory species, which can enrich the gas phase of warm interstellar environments.

We analysed the binding energy distributions and proposed a convenient way to compare the binding energies directly, by comparing these energies with an arbitrary fixed pre-exponential factor (A = 10¹² s⁻¹). The main difference in behaviour of these two molecules is probably because the entire binding energy distribution of formamide (E<sub>des</sub> = 5056–6990 K) is higher than the value of the amorphous water desorption (E<sub>des</sub> = 4810 K). On the contrary, the binding energy distribution of methylamine (E<sub>des</sub> = 3010–8420 K) is distributed over this value. There is no obvious link between the chemical functional groups (amino, hydroxyl, methyl, and carbonyl) and the binding energy distribution on our graphite template. The simple idea that all the molecules should desorb during the sublimation of the ice mantle is certainly unrealistic and illusive. The difference in the binding energies of formamide and methylamine could have an impact on the composition of the gas-phase environments, in particular in the coma of comets, but also in hot cores, hot corinos, and protoplanetary disks.

**Acknowledgements.** This work was supported by the Programme National "Physique et Chimie du Milieu Interstellaire (PCMI)" of CNRS/INSU with INC/INP co-funded by CEA and CNES. H.C would like to thank Prof. Darek Lis, Prof. Jean-Hugues Fillion of the LERMA team for their support and helpful corrections. The authors acknowledge the anonymous referee for constructive comments that greatly improved the paper. T.N. is granted by the LabEx MICHEM. Formamide is a target molecule of SOLIS, a NOEMA key programme led by C. Ceccarelli and P. Caselli.

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