Ice coverage of dust grains in cold astrophysical environments

Surface processes on cosmic solids in cold astrophysical environments lead to gas phase depletion and molecular complexity. Most astrophysical models assume that the molecular ice forms a thick multilayer substrate, not interacting with the dust surface. In contrast, we present experimental results demonstrating the importance of the surface for porous grains. We show that cosmic dust grains may be covered by a few monolayers of ice only. This implies that the role of dust surface structure, composition, and reactivity in models describing surface processes in cold interstellar, protostellar, and protoplanetary environments has to be reevaluated.


Introduction
Dust grains play a central role in the physics and chemistry of interstellar and circumstellar environments. They influence the thermal properties of the medium by absorption and emission of stellar light, provide surfaces for chemical reactions responsible for the synthesis of a major part of important astronomical molecules from the simplest ones such as H2 and H2O to complex organic molecules (COMs), e.g. sugars and alcohols, and they are building blocks of comets, asteroids, planetesimals, and planets.
It is well known that dust grains in cold cosmic environments such as molecular clouds and protostellar envelopes and planet-forming disks beyond the snowline are mixed with molecular ices. Typical sketches [1,2] show a compact dust core surrounded by a thick ice layer. The dust consists mainly of carbon-and silicate-based compounds [3,4] and the ice includes H2O (the main constituent accounting for more than 60% of the ice in most lines of sight [5]), CO, CO2, NH3, CH4, CH3OH and a number of minor components [6,7]. There is a remarkable diversity in the mixing ratios of molecular ices in interstellar and circumstellar environments.
Abundances for some species with respect to H2O range within more than an order of magnitude. The same is true for cometary ices [8].
Ice column densities are calculated from the band areas of their astronomically observed vibrational transitions using appropriate band strengths measured in the laboratory (see, e.g. [9]). These densities vary dramatically from object to object. The column density of water ice N(H2O) in prestellar cores and protostellar envelopes determined from the 3 µm band (the cleanest measure of the H2O ice column density) ranges from 0.3 × 10 18 to 12 × 10 18 cm -2 [10][11][12]. Assuming that ice covers a compact dust core and taking a typical value of 10 15 molecules per 1 cm 2 per monolayer, we can determine the coverage of grains by water ice to be in the range between 300 and 12000 monolayers (ML) depending on the grain size and the physical conditions (temperature, pressure) of the astrophysical environment. Physical and chemical processes occurring in such ices are barely sensitive to the properties of the dust surface.
On this basis, the majority of the laboratory experiments modelling physical and chemical processes on the surface of cosmic dust grains have been performed on thick multilayer ice mixtures (molecular solids) covering standard laboratory substrates, which might not be characteristic of cosmic dust grains. Adsorption, desorption, and reactivity of different molecules and radicals in molecular solids have been studied extensively during the last decades. We refer the reader to a number of review papers on these topics [1,[13][14][15][16].
Compared to molecular solids, there is a handful of studies of the physics and chemistry on the surface of dust grain analogs. We refer to recent papers on the formation [17,18] and desorption [19] of molecules. Summarising the findings of previous studies, it has been shown that (i) the efficiency of molecule formation depends on the morphology of the grain surface, (ii) the binding energies of species can be quite different for different grain surfaces and on the grain surfaces compared to molecular solids, (iii) functional groups and atoms of the grain surface can participate directly in surface reactions, (iv) the grain surface has a catalytic effect, (v) desorption kinetics and yields of volatile molecules are different for different grain surfaces and compared to molecular solids, (vi) water molecules can be trapped on the grain surface at temperatures above the desorption temperature of water ice.
Thus, dust grains play an important role in processes occurring on their surfaces. If the ice coverage of grains in molecular clouds, protostellar envelopes, and planet-forming disks is much thinner than what is typically assumed, the role of the grain surfaces in the physical and chemical processes in cold astrophysical environments is underestimated and the results obtained in the laboratory studies for molecular solids have to be evaluated in their astrophysical implications.

The porosity of dust grains
Analysis of cometary dust particles, dust evolution models, and laboratory experiments have indicated that grains in interstellar clouds, protostellar envelopes, and protoplanetary disks may be very porous meaning the existence of a very large surface.
There are a number of mechanisms responsible for the formation of dust grains in interstellar and circumstellar environments. First, nm-sized grains are formed in outflows of evolved stars and then distributed into the interstellar medium (ISM) [3]. Dust extinction observations and models indicate a very efficient growth of dust grains in the ISM (see, e.g. [4] for a review), especially in dense molecular clouds, where grains grow to fractal aggregates of submicronmicron sizes having a porosity of up to 80% [20]. Dust analog materials with the morphological characteristic of interstellar dust can be produced in the laboratory by gas-phase condensation of nm-sized amorphous carbon or silicate grains and their subsequent deposition onto a substrate, where they aggregate (see [21] for a detailed review). The morphology of such grain deposits, both carbon and silicate, can be understood as porous layers of fractal agglomerates having the porosity of up to 90% [22,23].
In the ISM, dust grains can be completely destroyed by supernova shocks. Estimations showed that only a few percent of the dust produced by stars survive in the ISM [24]. The second mechanism of the dust grains formation is a cold condensation at interstellar conditions. This mechanism was proved in the laboratory and the formation of fluffy, highly porous aggregates similar to the aggregates formed by gas-phase condensation was demonstrated [25,26].
In protostellar envelopes and planet-forming disks, grains continue to grow. The first stage of dust coagulation in disks leads to the formation of fractal aggregates of submillimetremillimetre size. Observations of protoplanetary disks suggest that the maximum size of dust grains is 1 mm at least [27]. Laboratory collisional studies (see [28] for a review) and models [29][30][31][32] showed that aggregation of µm-sized grain monomers leads to the formation of mmsized fluffy particles with a fractal dimension of 1 -2 and the porosity of more than 90%. In protoplanetary disks, such particles are believed to stick to each other due to molecular forces forming kilometre-sized planetesimals that, in turn, form planets due to their gravity. The formation of planets is often accompanied by the formation of debris disks around a central star [33]. In debris disks, a new, top-down mechanism comes into play. Small dust grains can be formed through collisional cascades started by collisions of planetesimals.
The high porosity of interstellar and protoplanetary dust grains is also suggested by the analysis of cometary dust particles. These particles should be the same materials that, mixed with ices, formed comets when the Solar system formed [34]. Analysis of radar [35] and in-situ [36][37][38][39] measurements of cometary comae, modelling of the light-scattering properties of the cometary dust [40], and analysis of the samples collected and returned by the Stardust mission [41] showed that cometary dust particles should present a mixture of dense and fluffy, highly porous aggregates. The fluffy particles are typically considered as fractal aggregates of nmsized grains that may be linked to interstellar dust. Such fractal particles can have microporosity of more than 99% [42].
Thus, there are indications of high porosity of dust grains in interstellar clouds, protostellar envelopes, and planet-forming disks. If this is true and the dust grains in these environments are highly porous particles, they have a corresponding large surface. The surface area of their laboratory analogs cannot be measured precisely but can be estimated.

The surface area of laboratory analogs of cosmic grains
Our recent laboratory experiments on cosmic dust grain analogs produced by gas-phase condensation and subsequent deposition onto a substrate have demonstrated that the surface area of aggregates of nm-sized grains can be several hundred times larger than the nominal surface area of the dust layer on a substrate, which can be seen as the surface area of an imaginary compact dust core. Our aggregates can be considered as analogs of dust grains in dense molecular clouds, protostellar envelopes, and planet-forming disks, for which they represent building blocks of larger aggregates having the similar structure (due to the fractal growth of grains) and porosity.
In our experiments, the formation of nm-sized amorphous carbon grains is performed by pulsed laser ablation of a graphite target and a subsequent condensation of the evaporated species in a quenching atmosphere of a few mbar of He + H2. The condensed grains are extracted adiabatically from the ablation chamber through a nozzle and a skimmer into a lowpressure chamber generating a particle beam. The beam is directed into the deposition chamber where the grains are deposited onto a KBr substrate. The deposited material is probed in situ by FTIR spectroscopy using a Fourier transform infrared (FTIR) spectrometer (Vertex 80v, Bruker) in the spectral range from 6000 to 400 cm -1 . For details of the experimental setup see [22,43]. The thickness of the grain layers is controlled by a quartz crystal resonator microbalance using known values for the deposit area of 1 cm 2 and a density of 1.7 g cm -3 .
In Figure 1 It was shown that water ice, having the nominal thickness of 400 ML or 130 nm (taking an approximate monolayer thickness of 0.3 nm [44]), mixed with carbon grains, thermally desorbs following the first-order kinetics of desorption. In contrast, the same number of water layers desorbs from pure KBr following the zeroth-order kinetics [43]. This result was explained by the desorption of a monolayer of water ice from a large surface of carbon grains. Therefore, the real surface of dust grains can be 400 times larger than the nominal surface of the dust layer. A similar result was obtained in another study, where the monolayer-multilayer transition for NH3+CO2 ices was observed at the nominal ice thickness of about 200 nm or 600 ML [17].    The dependence of the nominal ice thickness corresponding to the monolayer-multilayer transition on the thickness of the grain layer is presented in Figure 3. The growth of the dust layer should lead to an increase of the dust surface area, which depends linearly on the layer thickness. A deviation from the linear dependence should indicate a change in the porosity, which is definitely the case for the substrate change from KBr to carbon grains. For carbon grain layers with the thickness from 10 to 60 nm, the dependence is linear pointing to a constant porosity. The dust growth leads to an increased dust surface area and a corresponding larger number of molecules needed to cover this surface.
The further dust growth taking place in dense clouds, protostellar envelopes, and planetforming disks, which is hard to mimic in our experimental conditions, can lead to even larger number of molecules needed for one monolayer coverage on the surface of real cosmic grains.

Discussion
Different correction factors for the dust surface area were obtained using TPDs of different molecules: 400 for H2O [43], 600 for NH3+CO2 [17], and 200 for CO (this study). The carbon dust thicknesses in these three experiments were: 35 nm for H2O, 70 nm for NH3+CO2, and 60 nm for CO. It is clear that the correction factor is defined not only by the surface area but also by the surface properties, such as binding energy of molecules, number of available binding sites on the surface, hydrophobic and hydrophilic properties of grains, etc.
Applying the correction factor of 400 to the water ice thickness on cosmic grains of 300 -12000 ML, we obtain the coverage of grains by water ice in interstellar, protostellar, and protoplanetary environments in the range between 0.75 and 30 ML. Thus, in prestellar, protostellar, and protoplanetary phases, we might have ice layers ranging from a sub-monolayer to a few monolayers instead of a thick multilayer ice coverage on grains. In Figure 4, we offer a new sketch showing cosmic dust grains covered by ice molecules. Of course, such coverage cannot be homogeneous, and we should have clusters, islands, and voids.  Our results reinforce the recent proposition from Marchione et al. [45] that, in contradiction to the popular Onion model, bare dust grain surface in cold astrophysical environments would be available for other species except water to adsorb onto. The authors base their idea on the experimentally demonstrated agglomeration of H2O molecules on the dust surface [46] that may result in grain surfaces presenting both wet (H2O presents as agglomerates) and dry (absence of H2O) areas. In our case, the presence of wet and dry areas is simply due to the large surface of grains and its sub-monolayer coverage. A low ice coverage should not prevent agglomeration of H2O on grains and may even lead to a more efficient agglomeration due to the catalytic role of dust surfaces [17,47].
If dust grains in cold astrophysical environments are covered by ice layers ranging from submonolayers to a few monolayers, experiments such as the formation of CO and CO2 involving atoms of different carbon surfaces covered by H2O ice by UV, ion, and proton irradiation [48][49][50][51][52][53], the formation of formaldehyde H2CO by the addition of O and H atoms to bare carbon grains [18], and the formation of ammonium carbamate NH4 + NH2COO − in the thermal reaction CO2 + 2NH3 catalyzed by the surface of carbon and silicate grains [17,47] become extremely important. They should present more reliable pathways for the formation of molecules in surface reactions in interstellar clouds, protostellar envelopes, and planet-forming disks than the pathways obtained in experiments on molecular solids covering standard laboratory substrates.
Formaldehyde and ammonium carbamate are considered as precursors of prebiotic molecules. The origin of life on Earth is one of the most fascinating questions arising from the studies of our planet and the universe. There are two main hypotheses about the source of the organic compounds that could serve as the basis of life: their formation in the primitive Earth atmosphere [54,55] and in the ISM with a subsequent delivery to Earth on board of meteorites [56,57]. is a long-standing problem [58,59]. As much as a third of the total elemental O budget is unaccounted for in any observed form at the transition between diffuse and dense phases of the ISM and as much as a half is missed in dense phases. One explanation could be that oxygen is trapped with another equally abundant and reactive species, such as carbon and hydrogen, in the solid phase [58,60].
An understanding of all these astrophysically important processes can only be reached by a detailed surface characterization. The studies of physical-chemical processes on dust grains should be continued with an impact on astrochemical modelling involving dust surfaces.

Conclusions
Our new experiments on the temperature-programmed desorption of CO ice from the surface of laboratory analogs of cosmic carbon grains confirmed the results of the previous studies. Due to the high porosity of the grains, the surface area is a few hundred times larger than the surface of a KBr substrate, on which the ices are normally deposited. The surface of the substrate can be considered as the surface of the grains seen as a compact dust core. On the basis of our results, we propose that dust grains in cold astrophysical environments may be covered by only up to a few monolayers of molecular ices instead of hundreds of monolayers as it is typically assumed. A low ice coverage makes the role of dust grains in the surface processes much more important compared to the case of the thick ice mantle. With this letter, we would like to point the attention of the astrophysical and astrochemical communities to the necessity of further experimental and theoretical studies of physical-chemical processes on the surface of reliable cosmic dust analogs.