H2 Formation on Interstellar Grains - ACS Publications - American

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H2 Formation on Interstellar Grains Gianfranco Vidali* Syracuse University, 201 Physics Building, Syracuse, New York 13244, United States (number density n ≈ 1−102 atoms/cm3) where UV radiation penetrates the clouds, mostly diatomic and a few larger molecules are detected. The most abundant molecule, molecular hydrogen, long predicted to be in space6 was first detected only in 19707 using a spectrometer aboard a rocket. Molecular hydrogen is present ubiquitously in the interstellar medium: in diffuse clouds, dense clouds, where most of the atomic hydrogen has been converted into H2, PDRs (photodissociated regions), shocked regions, in jets, supernova remnants, and active galactic nuclei.8−10 The first proposal that H2 is made not in the gas-phase but on interstellar dust CONTENTS goes back to 1948,11 while the first experiments to verify the mechanisms of its formation in simulated space environments 1. Introduction 8762 were done only in the late 90s, fifty years later.12,13 In this 1.1. The Molecular Hydrogen Problem 8763 review, I will present an account of what we learned from 1.2. Need for Dust Grains 8763 experimental and theoretical work on the formation of H2 on 1.3. Cosmic Dust 8764 interstellar grain analogs. Despite the considerable progress (for 1.4. Mechanism of Reactions at Surfaces 8765 example, a few reactions on grains are now included in the most 2. Theory: Methods and Results 8766 advanced simulation codes of the chemical evolution of 2.1. H Interaction with Graphite, Amorphous interstellar clouds14−20) our knowledge on this subject is far Carbon, and PAHs 8766 form satisfactory, and I’ll point out where advances are needed. 2.2. Hydrogen on Silicates 8767 The formation of molecules in space occurs under unusual 3. Experiments: Methods and Results 8768 conditions. Because of the low density and low temperature, 3.1. Experimental Methods 8768 encounters between atoms/molecules are rare, and the 3.1.1. Equipment 8768 reactions that can take place need to have no activation 3.1.2. Measuring Methods 8769 energy. In most environments of the interstellar medium 3.2. Selected Results of H2 Formation on Dust (ISM), the space between stars, the number density is so low Analogs 8771 that three-body reactions are irrelevant. Rather, molecule 3.2.1. Formation of H2 on Bare Surfaces 8771 formation occurs via ion−molecule (H2+ + H2 → H3+ + H, 3.2.2. Formation of H2 on Ices 8774 rate coefficient k = 10−9 cm3/s), dissociative recombination 3.2.3. Ro-Vibrational Excitation 8775 + (H3 + e → H + H2, k = 10−7 cm3/s), and neutral−neutral (k = 3.2.4. ortho-to-para Ratio 8776 10−12 cm3/s) reactions, to name the most important types of 4. From the Laboratory to Interstellar Space 8776 reactions.8,21 Rate coefficients are usually parametrized in the 5. Challenges 8778 following form: k = A(T/300)Bexp−(C/T). Compilations of these Author Information 8778 Corresponding Author 8778 parameters A, B, and C can be found in databases that are used Notes 8778 to run simulations of the chemical evolution of ISM Acknowledgments 8778 environments (see, for example, the UMIST Database for References 8778 Astrochemistry (http://www.udfa.net/), The Ohio State University network (OSU; http://www.physics.ohio-state. edu/∼eric/research.html), and KIDA (http://kida.obs.ubordeaux1.fr/)22−25). Nowadays, a code using rate equations 1. INTRODUCTION to follow the chemical evolution of a cloud over its lifetime The first detection of molecules in space (CH, CH+, and CN) (tens of million years) has several thousands reactions and occurred in the late 1930s. Since then over 180 different hundreds of reactants in its database. Despite the great progress molecular species have been detected (http://www. achieved in compiling these databases, there are many astrochymist.org/), and the large majority are found in dense uncertainties stemming from the fact that reactions are usually clouds (number density n ≈ 104 atoms/cm3) or in “hot cores”, studied at much higher temperature than the one of interest the space surrounding a newborn high-mass star (greater than 5−8 solar masses),1,2 and in “hot-corinos”, the space around a Special Issue: 2013 Astrochemistry low-mass star.3−5 In the latter, the UV radiation from the new star drives the desorption of molecules from ices that coat dust Received: March 13, 2013 grains, and reactions take place in the gas. In diffuse clouds Published: October 25, 2013 © 2013 American Chemical Society

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their interest. Reviews of the formation of molecules on surfaces of astrophysical interest appeared recently.40−43 Review articles on specific topics are listed in the appropriate sections. The Proceeding of the Workshop H2 in Space held at the Observatoire de Paris in 1999 contains useful background articles.34 Recently published monographs about cosmic dust and physical/chemical processes in the interstellar medium are also useful starting points for more in-depth readings.8−10,44,45 This review is not about listing all works on H2 formation on surfaces but rather is about summarizing the status of the field with the most relevant contributions. Unfortunately, after about 15 years of research on the formation of H2 in space, it is not uncommon to read in the astrophysics literature that “we do not understand surface reactions in the interstellar context” without further qualifications or reference to 15 years of work. This is factually wrong. Thus, in this review emphasis is given in placing signposts, that is theoretical or experimental results that have helped clear our understanding of the problem of formation of molecular hydrogen in space.

here, and that these databases have still relatively few reactions involving the formation of molecules on grains. Molecular hydrogen, H2, has a very low rate coefficient for radiative association, 10−29 cm3/s,8 since the proto-molecule has to make a spin forbidden transition to the ground electronic state (X1Σ+g ) from a dissociative state (b3Σ+u ). The importance of understanding how molecular hydrogen is formed in space is 4-fold. First, H2 is the most abundant molecule and is observed in virtually every ISM environment. Therefore, we need to know enough of its formation chemistry that our predicted abundance in various environments matches the ones obtained from observations.26−28 Second, its transitions, charge status, and kinetics serve to characterize the medium in which it is.29,30 Third, by absorbing UV radiation and reradiating it in the infrared molecular hydrogen helps the cooling of a gravitationally collapsing cloud, thus facilitating the formation of stars.31,32 The connection between H2 and star formation comes from the Kennicutt-Schmidt (K−S) relation33 that relates the surface density of star formation to the surface density of hydrogen. It is used for computational models of star formation. Fourth, either in neutral or ionized form, it enters most networks to form other molecules.8,34 This review is structured as follows. In the remainder of this section, background material about the topic of this review, the formation of molecular hydrogen on dust grains, is introduced. It is now understood that most of H2 in the ISM is made on grains by the interaction of two neutrally charged hydrogen atoms that become trapped on the grain surface. There are other channels of H2 formation, such as the ones that involve high-energy processing, as in the interaction of cosmic rays with ices coating grains. For example, MeV ions were used to irradiate ices and H2 formation was detected. The H2 formation rate was evaluated in dense ISM cloud environments.35 In the irradiation of methane and deuterated methane ices at 11 K with 5 keV electrons mimicking the effect of cosmic rays, H2 or D2 was observed to evolve in a slow warm up of the methane ice.36,37 In the interaction of UV photons with water ice, H2 is formed via an abstraction mechanism (H + HOH → H2 + OH) and hydrogen recombination of hydrogen atoms detached from water by the UV photons (H + H → H2).38 Some of the hydrogen atoms might retain super thermal energies. To obtain rates from these experiments is not easy.35,37 These reactions will not be discussed further, although they are important in the overall chemistry of a cloud.39 Section 2 is about the theory and modeling of processes of hydrogen interaction with surfaces of interest in astrophysics and of the mechanisms of molecular hydrogen formation. In section 3, the experimental methods are presented first, and then they are followed by a review of the most important results of experiments on molecule hydrogen formation on dust analogs that took place in the last 15 years. This latter part is divided in results of H2 formation on bare grains (carbonaceous and silicates) and on ices. Results about the detection of rovibrational states of the nascent molecules and of the ortho-topara ratio are dealt in separate subsections because of their relevance to astronomical observations. Section 4 looks at theoretical and computational work that allowed experimental and theoretical results to be applied to study the chemical evolution of interstellar environments. Section 5 lists the challenges that await experimentalists, theoreticians, and observers who are interested in H2 formation in space. It is inevitable that there are going to be some repetitions, since it is expected that many readers will skip to the Section of

1.1. The Molecular Hydrogen Problem

If two neutral hydrogen atoms collide, they can end up in a vibrational level of the ground electronic state above the dissociation limit (ν> 14). To stabilize the molecule, a transition to the ground state is necessary but highly improbable because is slow; alternatively, the protomolecule can end up in the b3Σ+u electronic state. However, the transition to the X1Σ+g ground state is highly forbidden8 because of the different spin states of b3Σ+u and X1Σ+g . The rate of formation is constrained by the current observed abundance and the known rates of destruction by cosmic rays and photodissociation. Specifically, the rate coefficient of molecular hydrogen formation R (cm3/s) is related to the total number density n (in cm−3) of hydrogen atoms (both in atomic and molecular forms) n = nH + 2nH2 and the photodissociation rate β = 5 × 10−10 s−1 by8 RnHn = 0.11βn H2

(1)

From an analysis of the data from the Copernicus satellite, Jura26 found that the rate coefficient of H2 formation in diffuse clouds is 10−17 < R < 3 × 10−17 in cm3/s units. Since then, Gry et al.27 calculated the formation rate of H2 in the diffuse ISM using FUSE data, while Habart et al.28 using SWS-ISO data looked at photodissociated regions.46 Although the latter determination obtained in moderately excited PDRs gave a number a factor 2 to 5 higher, the overall agreement of these data is remarkable. Since the radiative association of two H atoms has a very small rate coefficient, it is clear that other routes to form molecular hydrogen must exist. Reaction involving ions are fast. For example: H + e → H− + hv

(2)

H− + H → H 2 + e

(3)

This reaction was responsible for the formation of H2 in the early Universe when grains were not yet present.47 However, in the present Universe, the ionization is low enough that there are not enough electrons to make this reaction important in H2 formation. 1.2. Need for Dust Grains

As first proposed by van de Hulst11 and then developed in a theory by Saltpeter and colleagues48,49 the solution to make enough molecular hydrogen was to consider grains as catalytic 8763


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atoms could fall into deep adsorption energy sites, mobility was greatly decreased and so the probability of making H2. Smoluchowski’s grains were actually closer to the current understanding of grains in dense clouds than the polycrystalline water ice grains of Salpeter’s model. Unfortunately, Smoluchowski’s model predicted a much smaller rate of H2 formation than the one required by observations.

sites. Although in space there is on average only one dust grain for every 1012 hydrogen atoms, and thus the probability of an H atom of hitting a dust grain might be low, once an H atom lands on a grain, the probability of encountering and reacting with another one can be high, and it becomes even higher for lower temperature of the surface of the grains (see Figure 1).

1.3. Cosmic Dust

Rapid progress in surface science, and especially in the interaction of atoms or molecules with surfaces, was obtained in the 1980s and 1990s in part due to availability of ultrahigh vacuum techniques and the use of single crystal surfaces for which cleaning and characterization methods could be readily established. The challenge of the study of reactions on cosmic dust analogs reside in the poor knowledge of the actual cosmic dust and in the fact that samples need to be of complex morphological and chemical composition, thus complicating both experimental and theoretical studies. We know about cosmic dust chiefly through observations. The presence of dust in the ISM was deduced because it “reddens” starlight; that is, it absorbs and scatters more effectively shorter wavelength (UV) than longer wavelength (IR) radiation.54 Interstellar dust was isolated in meteorites, but otherwise the dust obtained by instruments on satellites, such as StarDust, is mainly composed of interplanetary particles which on average are much bigger than interstellar dust grains.55 Modeling based on observation of scattered light has shown that the average grain has a diameter of 0.1 μm and an analytic empirical relation gives the size distribution Na ≈ a−3.5, where a is the radius of the grain,56 in the range 0.005 μm < a < 0.25 μm. The composition of dust is deduced from the observed abundances in the gas phase, where severely depleted elements, such as Fe and Si, are believed to be in condensed matter, i.e., dust grains. From infrared observations, it is found that Si and O are bound in silicates that have Si−O tetrahedra, the olivines, ((MgxFe1−x)2SiO4, 0 < x < 1) or are bound as in pyroxenes, ((MgxFe1−x)SiO3, 0 < x < 1),57 while carbon is likely to be in graphitic and amorphous forms. The average temperature of grains is in the 10−20 K range in dense clouds and higher (15−30 K) in diffuse clouds. Because of the low heat capacity, small (∼100 Å) grains are subject to large temperature spikes when hit by photons.45 Stardust is made in outflows of stars in the AGB (Asymptotic Giant Branch) phase where the copious gas ejected by the star condenses in the expansion.58 Dust is also made in supernovae ejecta.59 The dust that is found in ejecta of stars or in protoplanetary disks around young stellar objects contains material, such as crystalline silicates and SiC, that is not found in the ISM, indicating that dust in the ISM goes through radical transformations due to shock waves, grain−grain collisions and other processes.60,61 Also, the estimated survival time to dust destruction due to supernovae and other processes is as much as 1 order of magnitude shorter than the injection time, implying that dust is made (or remade) in the ISM. In laboratory work, see refs 62−65, the comparison of infrared reflectance/absorption data of prepared samples with observations in the infrared of interstellar clouds helped the modeling of ISM dust. It is now accepted that silicate grains in the ISM are glassy/amorphous,66 elongated, and “fluffy” with a large surface area. Carbonaceous material can take many forms, such as nanodiamonds, graphite, fullerenes, and kerogen.67,68 PAHs (polycyclic aromatic hydrocarbons) are molecules made up of

Figure 1. Cartoon of the interaction of hydrogen atoms with a dust grain. Reprinted with permission from ref 40. Copyright 2013 Springer.

The average time of an atom on a surface is given by ⎡E ⎤ t = τ exp⎢ des ⎥ ⎣ kBT ⎦

(4)

where τ = (h/kBT)Z (h is the Planck’s constant, kB is the Boltzmann’s constant, and Z is the internal partition function), Edes is the activation energy for desorption, and T is the temperature of the surface. A typical value for τ is ∼10−12 s. For Edes ≈ 450 K, a value of H interaction with water ice,49 the residence time is of the order of the time between arrivals of H on a surface of a dust grain in an ISM cloud, which is the inverse of the arrival rate of particles that actually stick on a grain:

dN = ξvHnHσ (5) dt 3 2 Typical values are nH = 100 atoms/cm , σ = πa = 3 × 10−10 cm2 is the (geometrical) cross section of an average grain (a = 0.1 μm), ξ = 0.3 the sticking coefficient, and vH = 1000 m/s the speed of H atoms.50 As Salpeter and colleagues realized51 the formation of H2 would be strongly restricted by the value of the hydrogen-surface interaction energy. It would also imply that molecular hydrogen could be formed only in very specific environments where the temperature of the grain and the Hsurface interaction energy are just so that H atoms spend an amount of time on the grain that is larger than the interval between successive arrivals of H atoms on the grains. A way out of this impasse was to consider a range of interaction energies between H and the surface, so the range in grain temperature over which there is successful H2 formation would be greatly widened. The requirement of having a distribution of energy values could be justified by considering that surfaces of crystalline water ice, the model of grain considered by Salpeter and others, are disordered. Smoluchowski52,53 went a step beyond and assumed that the ice is amorphous. Because H 8764


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Figure 2. AFM images and line scans of single crystal silicate (left) and an amorphous silicate (right). From He et al.,71 with permission of the Royal Chemical Society.

Experiments of thermal energy H and H2 beam scattering from a single crystal graphite surface gave results comparable to the ones above, that is an energy of the ground state of the atom/molecule-surface potential of 31 and 42 meV (366 and 482 K), respectively.82,83 These calculations and experiments implied that the H interaction with surfaces of materials representing dust grains is of physisorption, which means it is governed by weak van der Waals forces with little sharing of electrons between the adsorbate and the surface.84 A compilation of the characteristic parameters (well depth, ground state, atom-surface equilibrium distance) of the interaction of light atoms/molecules (H, H2, D, D2, and He) with many surfaces was done by Vidali et al.85 The calculations of Hollenbach and Salpeter gave fast diffusion for H atoms, chiefly due to tunneling. Therefore, the mechanism of H2 formation was consistent with the familiar Langmuir−Hinshelwood processes of reaction, i.e., accommodation of the gas-phase particle with the surface, diffusion, and reaction with another partner. However, early calculations of H interaction with the basal plane of graphite showed that an H atom would strongly bind on top of one of the C atoms of the graphite hexagons (see section 2). It was also shown that another H atom approaching the H-covered graphite surface would bind directly with one of the H chemisorbed atoms without prior accommodation with the surface. A bond would form between the two H atoms and the H2 molecule so born would leave the surface in translational and ro-vibrational excited states. Thus, according to these calculations, the mechanism of formation of H2 on graphite is the Eley−Rideal one, sometimes called “prompt reaction”.86 The Eley−Rideal reaction mechanism87 was shown to operate in several cases of H (or D) interaction with single crystal metal and semiconductor surfaces,.8889 One of the characteristics of this mechanism is the small cross-section, which is typically of the order of Å2. The cross-section is determined by monitoring the formation of molecules as a function of irradiation time of atoms on the surface. For example, in a typical experiment a quadrupole mass spectrometer is placed in front of the surface precovered with H atoms. As hydrogen atoms are sent to the surface, molecules

attached benzene rings, similar to a section of a graphitic sheet. PAHs represent a class of cosmic material between molecules and grains.69,70 See Figure 2. First detected in the ISM in 1973,72 but suspected to be present long before, ices are an important reservoir of molecular mater.18,73−76 In dense clouds, away from UV radiation, grains are colder than in diffuse clouds and covered with a layer of ice that can be a few hundred Å thick. Most of the ice is made of water molecules, but there are significant fractions of CO2, CO, CH3OH, CH4, and H2CO.73 The relative composition depends on the particular cloud, and various models appeared in the literature.77 The morphology of water ice is obtained through the study of the 3.06 μm band and other infrared features.78,79 Ices grow through condensation of gas-phase species and by reactions of and with atomic species, i.e., mostly hydrogen and oxygen; ice composition evolves due to atom/molecule aggregation, reaction among different species and UV and cosmic rays processing. This makes ices an important locus of molecular complexity.41,43,75,80 1.4. Mechanism of Reactions at Surfaces

Hollenbach and Salpeter calculated the van der Waals-like interaction of a hydrogen atom with the surface of water ice and found a potential energy well depth of 450 K.49 They realized that they needed enhanced adsorption sites to hold H atoms long enough to encounter another H atoms on the small surface of a grain. The area σ of an “average” grain of diameter 0.1 μm is ∼10−10 cm2; the interval between the arrival of H atoms in a diffuse cloud (100 atoms/cm3, kinetic temperature of ∼50 K) is a few hundred seconds, see eq 5, (dN/dt)−1 = (ξnHvHσ)−1, while the residence time of an H atom is of the order of a few hundred seconds for T = 10 K, but it is already of the order of a second at T = 18 K, see eq 4, t = τ exp [Edes/kBT] where τ is taken to be 10−12 seconds. Buch and Zhang81 calculated the potential energy minima and diffusion energy barrier of H on the surface of an amorphous water-ice cluster. They found that the minima are centered around 350 K with a bell-shape distribution ranging approximately from 250 to 700K, plus a small shallower set of states around 100 K. 8765


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of the hexagon. On the other hand, the experiments with beams of H and H2 at thermal energies scattered from a single crystal graphite sample showed that the interaction is weak, with ground state energies of the H- and H2-graphite potential of 32 and 42 meV, respectively.82,83 The experiments at UCL on the formation of H2 and HD on HOPG (highly oriented pyrolytic graphite), see ref 104 and references cited therein, seemed to be compatible with the earlier experimental results, although the UCL experiments were designed to study the ro-vibrational excitation of the molecule and not the details of the H-surface interaction, see section 3.2.1. Most calculations of the H-graphite interaction use DFT (density functional theory),105−109 but earlier calculations used also classical or quasi classical formalisms.110−113 Improvements in the application of DFT to atom-surface interaction has led to a more accurate handling of the interaction at large distances where weak dispersion-like forces should dominate. Jeloaica and Sidis114 used gradient-corrected spin-polarized DFT to calculate the H-graphite interaction. The potential has both a physisorption well (although deeper that the experimental value82) and a chemisorption well. Separating the two is a small (∼0.2 eV) energy barrier for the H atom to move into the chemisorbed state. The preferred site for chemisorption is above a C atom that puckers out by ∼0.35 Å and changes its hybridization to sp2/sp3. Experimental confirmation of this effect was reached recently.115 The issue of hydrogenation of graphite and dehydrogenation by atomic oxygen was considered by Allouche et al.116 using a similar formalism. In these DFT calculations108,114 of the H-graphite interaction H binds to a C atom with ∼0.67 eV of energy. Subsequently, accurate quantum calculations confirmed this picture and gave accurate values of the adsorption energy and diffusion energy barriers.117−119 A recent study examined the role of the surface relaxation and how it is handled computationally. 119 Furthermore, when more than one H atom is adsorbed on the surface, there are changes in the H-surface interaction and in the H2 formation processes.120 Theoretical studies105,106,108−110,120−128 of H2 formation concentrated on exploring the Eley−Rideal mechanism of H atoms on the basal plane of graphite. (Henceforth, we will use the term “graphite” although calculations are sometimes done on a partial sheet of graphite, whether hydrogenated, such as coronene, or not, and, more recently, on graphene. Coronene consists of 7 benzene-like rings arranged as in graphite; graphene129consists of a single sheet of graphite.) Farebrother et al.105 used DFT to calculate the formation of H2 and found that H2 comes out mostly in the vibrational state ν = 2. Later works calculated also the formation of H2 from H atoms which are trapped in the physisorption well of the H-graphite potential.130,131 Sha et al.107 used DFT electronic structure calculations and quantum scattering studies to calculate the cross-section Σ of H2 formation in both the case of H chemisorbed (Σ ≈ 8 Å2) and H physisorbed (Σ here is strongly dependent on incident energy) on the graphite surface. In the former case, there is substantial (∼1 eV) translational energy of the departing molecule, while in the latter hardly any, but in both there is high vibrational excitation. To frame this discussion using a more general viewpoint, the surface science literature indicates that experimentally and theoretically the Langmuir−Hinshelwood mechanism is favored over the Eley− Rideal one.132 As mentioned earlier there is a keen interest in knowing the ro-vibrational state of the desorbing molecule, since it has an

form promptly and desorb due to the excess energy released in the reaction. This signal decreases exponentially as the H precovered surface gets depleted of H atoms: ∼e−ϕ∑ t where ϕ is the flux of incoming H atoms, Σ is the reaction cross-section, and t is the time. Besides the cross-section, evidence of the E-R reaction can be found by measuring the ro-vibrational energy of the molecule departing the surface.90 The molecule is expected to be in a highly ro-vibrational state, although there is a range of theoretical predictions about the state of the molecule (see section 2.0.1). In certain experiments, a larger value of the cross-section was measured (tens of Å2).91 Another mechanism, called “hot atom”,87 was postulated for explaining this larger value of the cross-section Σ. This model consists in assuming that the incoming atom upon impact with the surface skitters on the surface at hyperthermal speed before encountering another H atom; this is a different mechanism than the one of making a direct hit with with the adsorbed atom as in the Eley− Rideal process. After making a bond it leaves the surface as an excited molecule. Whether one system shows the Eley−Rideal mechanism or the hot-atom mechanism is sometimes not so easy to determine,92 but, since actual dust grains have few H atoms on their surfaces at any given time, it might consequential in formulating a theory of molecular formation on actual dust grains. As the interaction of H or D atoms with surfaces of analogs of cosmic grains is concerned, the E-R/“hot atom” mechanism was invoked to explain the formation of HD from H-loaded amorphous carbon,93 of HD and D2 from graphite,94−97 coronene,98,99 and tholins,100 and of D2 from an amorphous silicate film;101 details are in section 3.2.

2. THEORY: METHODS AND RESULTS As mentioned in the Introduction, it is convenient to consider two types of interactions between an atom and a surface: physical adsorption, or physisorption, and chemical adsorption, or chemisorption. The first involves long-range dispersion forces and the characteristics energies are in the tens to a few hundred meV, while chemisorption is about eV energies and chemical bonding.87 Obviously, this is just a coarse way to categorize an otherwise wide range of complex interactions. The types of analogs of interstellar dust of interest here are silicates, carbonaceous materials (such as graphite, graphene, nanodiamonds, PAHs, etc.), and ices deposited on them. For the H-polycrystalline ice interaction, Hollenbach and Salpeter used a pairwise sum of H-water molecule potentials, obtaining an energy well-depth of the interaction potential of about 450 K.102 The calculation of Buch and Zhang81 of the interaction of H with an ice cluster of 115 water molecules gave a result in the same energy range (see section 1.4). The energy barrier for diffusion is in the range of 50−650 K. 2.1. H Interaction with Graphite, Amorphous Carbon, and PAHs

There has been a prolific effort to study the interaction of atomic and molecular hydrogen with graphite and carbonaceous material. Here, the theoretical studies most relevant to the formation of molecular hydrogen in space are considered. The following topics are reviewed: atom-graphite interaction, H2 formation via the Eley−Rideal mechanism, ro-vibrational excitation, diffusion, and sticking of H atoms. Aronowitz and Chang,103 using an extended modified Hückel program, calculated that in the interaction of an H atom with the basal plane of graphite the H atom chemisorbs at the center 8766


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show that the H atom can travel for tens of Å on the surface of ice before coming to rest,147,149 the specific value depending on the incident energy of the atom. Matar et al. obtained an analytical formula for the sticking of H, D, H2, and D2 on ice surfaces as a function of hydrogen kinetic energy based on an analysis of experimental data.150 Another important process in the formation of an H2 molecule is the facility with which an H atom can move on the surface. Here there is a competition between the holding potential for the chemisorption state and the energy required to move to the next site. Different groups have obtained quite different results; in some calculations, an energy barrier to diffusion turns out to be higher than the energy to desorb.151,152 Because of the computational complexity in obtaining diffusion of H atoms using first principle calculations, the preferred method is still molecular dynamics, which uses classical physics but is improved and checked with selective first-principle calculations.153 Petrucci et al.154 calculated the diffusion of H2 on graphene using molecular dynamics and a semiempirical interaction potential that reproduces the H2graphite results of Mattera et al.83 In recent years, there has been a keen interest in studying PAHs, as they are believed to be abundant and to be the carriers of the Unified Infrared Bands and perhaps (although this is not completely established) of the 2175 Å “bump” which is a feature in the UV part of the extinction (scattering plus absorption) by small grains;70,155 this “bump” is believed to be due to a material with π−π bonding, such as a graphitic material. Furthermore, the possibility that they can be a contributor to H2 formation has been entertained.28,156,157 Rauls and Hornakaer158 used DFT to show that on neutral PAHs molecular hydrogen can form via superhydrogenation, or adsorption of hydrogen on nonedge C atoms. Experiments on the formation of H2 on hydrogenated and superhydrogenated PAHs are discussed in the section “Formation of H2 on Bare Surfaces”.99

impact on astrophysics and astronomical observations. There is quite a range of prediction on the ro-vibrational state of molecules formed via the Eley−Rideal mechanism on a graphite surface depending on the specific calculation method, such as whether the surface is allowed to relax,112,124,125 and on the energy of the incoming H atom before the reaction.113 When two H atoms are lightly adsorbed on a graphite surface, the H2 molecule resulting from their interaction is in a highly (ν ≈ 8− 12) quantum vibrational state.130,131,133 In summary, the population of vibrational level is not necessarily Gaussian and sometimes is bimodal, with typical vibrational quantum number ν between 5 and 11, depending on how the remaining energy is partitioned between solid and translational energy, the energy of the incoming particle, the strength of the bond of the H or D atom on the surface, whether the collision is collinear or not, a n d w h e t h e r t h e r e a r e o t h er H a t o m s c h em isorbed.108−112,120,124−127 The inclusion of the zero-point energy of H on graphite in the semiempirical Bachelleire potential,126 which is derived from the Brenner potential134 that otherwise reproduces the puckering of the C-atom, produces broadening of the most populated ν levels but with ν < 5 and an increase of the range of populated J levels,135 although experiments show a narrower J range and low J values.104 Because carbonaceous materials in space have hardly perfect graphite-like surfaces, it is important to assess how defects and disorder in general affect the results obtained above on ideal surfaces. In a DFT-based study, the role of defects, such as pentagonal rings in the graphene lattice, in modifying H adsorption and H2 formation was calculated;136 interestingly, the introduction of defects lowers the energy barriers to diffusion which would otherwise be quite high. Another approach to study more complex situations, such as having more that one H atom on the surface or the formation of H2 on hydrogenated and super hydrogenated PAH (see also Section below) was to use MonteCarlo simulations with input from DFT calculations on key steps or processes in the H motion and H2 formation on a graphite surface.137 This method allows to look at more complex surfaces, such as ones with defects, or surfaces of small grains heated by UV radiation.138−140 Sticking and diffusion are two other processes that are necessary to be known in order to obtain rates of molecular hydrogen formation. The sticking of H atoms on graphite was studied by a few authors.141−145 Most recent work has been focused on the sticking of H on graphene. Because of the different phonon modes of graphite and graphene, the dissipation of energy for a low kinetic energy H atom that becomes trapped in the physisorption well is different for the two materials, graphene being more effective in trapping H.145 For an H atom in the physisorption well, accurate quantum calculations of sticking and desorption were carried out using different methods.117,118,145 At low collision energies ( 32 K. The coverage is below one layer, see ref 42 for details. From Vidali et al.42 Reproduced by permission of IOP Publishing. All rights reserved. 8772


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level ν = 4, and by TPD. The REMPI detection was used both during the irradiation of the sample with D atoms and during the TPD. The TPD was obviously carried out after the irradiation; see Figure 8. The ability of measuring at the same time the REMPI and TPD signal is key in discovering how really the formation of H2 occurs on grains as a function of the temperature of the silicate film, see Figure 9. While the TPD yield dropped to zero for irradiation with the surface above 17 K, the REMPI signal was detected up to the sample temperature of 70 K during the irradiation with the D beam. This remarkable result shows that are two processes taking place, one that makes molecules that desorb right away and that they are detected in a high (ν = 4, J = 2) vibrational state, and another where the molecules are either made right away and remain on the surface, or are made and come off during the TPD. Note that the molecule detected during the TPD are vibrationally cold, since there is no REMPI signal for ν = 4. The Lemaire et al. data show prompt desorption of D2 upon its formation on the silicate film, and thus it seems in contradiction with the results for Pirronello et al.12,13 Two facts need to be considered. First, assuming a distribution of molecules in the ν states as in HD formed on graphite,202 Lemaire et al. estimated that most molecules come off during the TPD, in agreement with Pirronello et al. results. Second, the silicates used in Pirronello et al. study were much rougher than the smooth film used in Lemaire et al. experiments. In the case of the former, AFM analyses show that in some films the roughness (trough to peak vertical profile) was as large as one micrometer . Gavilan et al.199 used REMPI and TPD to measure the effect that the precoverage with D2 molecules of a silicate film has on the formation of molecular deuterium. It is found, contrary to what one might have expected, that the formation is enhanced. The reason given is that the diffusion of D atoms on a surface with some D2 molecules already present is enhanced because the deepest adsorption energy sites (and consequently the ones with the highest energy barrier to diffusion) are already

Figure 7. Distribution of desorption energy of D2 from an amorphous silicate (top) and a single crystalline silicate (bottom). From He et al.,71 with permission of the Royal Chemical Society.

desorption energy for D2 is 27 meV. For an amorphous silicate sample, FeMg SiO4, using a model with three desorption energies for HD,174 the values are 35, 53, and 75 meV, and the energy barrier for diffusion of H atoms 35 meV. In both models, for obtaining the fit with the smallest number of parameters, no distinction was made between H and D. In practice, it is expected that H is more mobile than D.189 Notice also that the energy barrier to diffusion, assuming thermal diffusion, is a lower bound.174 See Table 1. Lemaire et al.101 measured the formation of D2 on an amorphous silicate thin film over a wide range of sample temperatures. The reaction product, D2, was detected in two ways, with REMPI, by measuring the molecules in vibrational

Table 1. Selection of Experimental Results of H2 (or HD or D2) Formation on Dust Grain Analogsa dust analog

ε

ΔT (K)

Edes (meV)

mech.

olivine (polycrys.) amorphous carbon amorphous water ice amorphous silicate amorphous silicate H-loaded amorph. carbon graphite (HOPG) graphite (HOPG) coronene tholin tholin

low high high high high

5−20 5−20 5−30 5−30 5−70 300 15 300 300 5−30 160−310

27 47 40−70 35−53−75

L-H L-H L-H, H-A L-H L-H, H-A E-R E-R E-R E-R E-R L-H

30−55

ro-vibr.

low

K.E.

Th

high high Hth

ref b c d e f g h i j k l

0 < ε < 1 is the formation efficiency, ΔT is the sample temperature range investigated, Edes is the desorption energy of H2 (or D2 or HD) (see references for specifics), L-H, E-R, and H-A refer to the Langmuir-Hinshelwood, Eley-Rideal, and hot-atom mechanisms, respectively, K.E. is the kinetic energy of the departing H2. Ro-vibr. describes the degree of ro-vibrational excitation. Additionally, some of the papers172−174,178,194,195 report the diffusion energy of H atoms; see the text and cited references for more information. “Th” is thermal, “Hth” is hyper-thermal (1-2 eV), and “Mech.” is mechanism. Adapted from ref 40. bPirronello et al.12 Analysis of data in Katz et al.172 cPirronello et al.187 Analysis of data in Katz et al.172 d Results depend on the type of water ice:196 (data: TPD),197 (TPD),198 (REMPI and TPD),199 (REMPI and TPD),195 (REMPI and TPD). Analysis in Perets et al.173 Kinetic data in Roser et al.179 (time-of-flight) and Hornekaer et al.180 (time-of-flight); ro-vibrational data in Hornekaer et al.,180 Congiu et al.,200 and Gavilan et al.198 eVidali and Li.190 Data: TPD. Analysis of data in: Perets et al.174 fLemaire et al.101 Data:TPD and REMPI. g Mennella.93 Data:TPD and IR. hIslam et al. and Latimer et al.104,201 Data: REMPI. Analysis is also in Islam et al.202 iBaouche et al.,96 laser assisted associate desorption; the temperature reported is the initial temperature; the final temperature after the laser pulse is 1200 K. jMennella;176 Thrower et al.203 Data: IR and TPD. kLi et al.185 Tholins are analogs of the aerosol particles in Titan’s atmosphere. Tholins are disordered chains of highly unsaturated polymers of type HxCyNz. Data: TPD and IR. lSekine et al.100 Data:IR and TPD. a

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Figure 8. REMPI-TOF signal (in black; in red, 25-points FFT filtering) shows the formation of D2 in the v″ = 4, J″ = 2 excited state when irradiating the sample at 12K with D atoms from time t = 0 to 600 s. In blue (scale offset): QMS D2 signal; its rise at t = 0 is due to the increased gas-load from the beam. In orange: sample temperature. During the temperature ramp of the TPD (beam valve closed), a sharp peak of D2 molecules desorbing from the surface is seen whereas there is no REMPI signal (the second broad and smaller peak during the TPD is an artifact due molecules desorbing from parts of the cryostat). When the temperature reaches 70 K, the irradiation resumes. The QMS signal goes to the same level as at t = 0 (which is due to the extra D2 gas load from the beam) while the REMPI signal is almost negligible. From Lemaire et al.101 Reproduced by permission of the AAS.

atmosphere. The hypothesis is then that atomic hydrogen has been used up in the formation of molecular hydrogen via catalytic processes on the surface of tholins. (The pressure where these events occur in the atmosphere of Titan is too low for three-body gas-phase recombination of hydrogen to occur). Sekine et al.100 did a study using, in two separate apparatuses, IR spectroscopy and mass spectrometry to measure the formation of molecular hydrogen on a tholin deposit at “high” temperature, at 160 K (the temperature of tholins in Titan’s atmosphere) and at 300 K. Through the changes in the IR spectra, they saw that bonds in the polymers became saturated by the arrival of H (or D) atoms and isotope exchange was observed as well; there were also processes of abstraction of H (or D). Li et al.185 instead measured the formation of HD on tholins at low temperature, T < 30 K, where the H or D atoms experience weak physisorption forces and the mechanism of reaction is the Langmuir−Hinshelwood one. 3.2.2. Formation of H2 on Ices. A good deal of effort has gone to studying the formation of molecular hydrogen with surfaces of water ice. Ices coat grains in dense clouds and are the repository of important radicals and molecules. In dense clouds, most of hydrogen is tied in molecules. Hydrogen is selfshielding and thus the inner part of a dense cloud is shielded from photodissociation of radiation coming from nearby stars, although not from the effects of cosmic rays.8,39 Ices are composed in large part of water, see section 1.3 for details, with significant percentages of CO2, CO, CH3OH, etc. The water ice phase diagram is rather complex. At low temperature and in vacuum, there are two amorphous phases, a high-density and low-density one.205 These two amorphous phases are also called somewhat imprecisely porous and nonporous or compact water ice. To make sense of this seemingly contradictory labels, one has to realize that “high-density” refers to the density of molecules in the ice. The density refers to the distance of oxygen atoms as measured by X-rays, but the ice itself is porous.205 The degree of porosity depends on the way it is

Figure 9. Integrated intensities of the REMPI (D2) signal during D irradiation and of the QMS (D2) signal of the TPD after D irradiation vs the sample temperature during irradiation. The HD signal is due to exchange reactions on the sample and/or walls of the apparatus. From Lemaire et al.101 Reproduced by permission of the AAS.

occupied by D2 molecules previously deposited. Analysis of TPD data after irradiation of the silicate with D2 show that the molecules occupy sites with energy in the range of 30−70 meV. This is in agreement with the data and model of Perets et al.,174 see above, and of He et al.71 Tholins is the name given204 to particles that are analogs of aerosol particles that are present in the atmosphere of Titan, one of the satellites of Saturn. Titan’s atmosphere is composed of nitrogen with a small percentage of methane. Energetic processes occurring in the stratosphere of Titan produce a rich variety of hydrocarbons that eventually coalesce in highly unsaturated and disordered polymers characterized by the generic formula CxHyNz. The unsaturated nature of these polymers suggests there is little atomic hydrogen in Titan’s 8774


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also in agreement with Amiaud et al.170 experiment where they found fast diffusion. In that case, because of the higher coverage, only the shallow adsorption sites were probed, since the deep adsorption sites were already all filled. 3.2.3. Ro-Vibrational Excitation. As mentioned elsewhere in this review, the characterization of ro-vibrational states of the newly formed molecular hydrogen on a dust grain analog is of great importance, both in chemical physics and in astrophysics. In the review of the theory, I reported the range of the predictions of some of the current theoretical model of the formation of H2. There seems to be a consensus that the molecule leaves the surface in a higher vibrational than rotational state, at least as graphitic surfaces are concerned; see section 2. As mentioned before, the most populated vibrational state depends on many conditions. For typical experimental conditions, a peak vibrational state in the range of ν = 5−10 is expected. The most extensive measurements were carried out at University College London, in Steven Price’s laboratory.177 The experiments were done by sending H and D low temperature beams on a graphite surface at low temperature (in most cases around 12 K). Using the (2 + 1) REMPI technique described above, they measured the rovibrational excitation of HD. The most populated ν states are 3−5, while the most populated rotational states are with J below 4.104,201,202 There was not a direct measurement of the translational energy, but Creighan et al. suggested, based on a time-of-flight filter, that it should be less than 1 eV.202,213 Since the work of Black and Dalgarno,214 who assumed that the energy released in the formation of H2 is equally partitioned between the solid and translation and vibration of the molecule, a few calculation of the IR emission spectrum of H2 due to formation pumping appeared in the literature (see Islam et al. for a review202). Takahashi and Uehara215 calculated the IR spectrum of transitions due to formation pumping on different kinds of surfaces, and they predicted that they should be observable. Islam et al.202 took the distribution in ν, J levels of HD obtained from the UCL laboratory and computed the expected IR transitions in interstellar clouds from the rovibrational spectra of H2 measured in the laboratory. They assumed that the ortho-to-para ratio, see section 3.2.4, is 3, that is the high-temperature limit. The spectra derived from “formation pumping” were then compared to the spectra obtained from UV pumping. They concluded that to observe signatures of formation pumping the best place would not be in dark molecular clouds where most of atomic hydrogen has been converted into molecular hydrogen. The reason is that there would be too much attenuation of the signal due to the cloud itself. Rather, they suggest to look in places where there is significant destruction of H2 due, for example, to X-ray sources. In such cases, the IR emission signatures from photon pumping would be due to molecules in lower vibrational states than in the case of molecules coming from grains, thus allowing for a separation of the two processes. See Figure 10. So far, no transition due to H2 formation pumping has been observed.216,217 Based on their laboratory results about the detection of molecules in ν = 4 coming from a formation process on a bare silicate grain analog, see section 3.2.1, Lemaire et al.101 suggested to look at transitions from ν = 4 to a lower ν in the X, J, and H bands at 1/1.25/1.65 μm in diffuse or dense clouds where grains are still bare. Such signatures will have to be separated from contributions of radiative or collision pumping.

measured, see below. The study of H2 formation on water ice has been the source of some controversy centered on whether the hydrogen molecules are formed during the irradiation170,180 or afterward, during the TPD, as results from another laboratory197 and computer simulations173 indicate. The reason for the difference in interpretation might reside in a few factors, such as ice preparations, fluxes of hydrogen atoms, and broadness of TPD features that lends to ambiguities of interpretation. Vidali et al. showed that a factor 10 in H-atom fluxes typically used in laboratories can lead to two different physical situations on the ice.206 According to calculations based on molecular dynamics an H atom lending on water ice from the gas phase can move on a surface for tens of angstroms before coming to a stop.207,149 If the flux and coverage are sufficiently high (and similar to the ones used in some experiments), but still well below the monolayer coverage, then there is a good chance that the atom that just landed on the surface will encounter another one and form a molecule. Vice versa, in the case of low flux and coverage, it is much more likely that the H atom, on a low ( 200 K), the OPR is close to 3. At low temperature OPR for H2 approaches 0 (all H2 molecules are in the J = 0 state). A departure of this value from 3 contains useful information. For example, a value significant lower that 3 would imply that H2 had time to undergo spin conversion in a region where the temperature was much lower than 200 K. It has been used to study postshocked regions through the para to ortho conversion219as well as the age of dark clouds or the abundance of deuterated species through the chemistry that is influenced by the OPR of H2. The J = 1 state is at a level 170 K higher than the J = 0. A proton-exchange reaction releases that energy with consequences for ISM chemistry, notably deuteration.221,222 Deviations from LTE (local thermal equilibrium) were reported in a variety of objects: starburst galaxies,223 galactic molecular clouds, 224 Herbig-Haro outflows, 225 shocks,226−228 and photodissociation regions.229,230 A big question is whether the formation of H2 on grains yields H2 with OPR in equilibrium with the temperature of the surface or in the high temperature value of 3. Obviously, if the H2 formation has a characteristic value, then it would be easier to spot the formation of H2 on grains in the ISM. The measurement of the OPR in the laboratory has been made

4. FROM THE LABORATORY TO INTERSTELLAR SPACE Measuring molecule formation on grains as well as the physical/chemical processes associated with it, such as sticking, diffusion, and energy partition, is just the first step. A straightforward use of laboratory results to study actual processes in the interstellar medium might not be possible, for reasons that have been mentioned before: 1. Experiments are done with fluxes of atoms that are easily 4 or 5 orders of magnitude higher than the one present in the interstellar medium. 2. Dust grains have a distribution of sizes. 3. The processes occurring in space take place on different time scales than in the laboratory. For example, the formation of molecular hydrogen in space occurs in approximately steady state conditions (vs respect to the time scale of many processes occurring on surfaces, such as sticking or desorption, which are much faster), while this is not always the case in laboratory settings. In the laboratory, a typical technique used in these studies in thermal programmed desorption which probes kinetic processes and is clearly done in nonsteady state 8776


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conditions. Laboratory results are essential in the study of the chemical evolution of ISM environments. Computer codes that trace the chemical composition of an interstellar cloud nowadays incorporate processes that occur at surfaces of grains, not just restricted to the formation of molecular hydrogen, but also to the formation of other molecules (formaldehyde, methanol, etc.). Katz et al.172 used rate equations to extract from TPD traces the energy barriers for diffusion of atomic hydrogen and for the desorption of molecular hydrogen. They obtained the following des des values: Ediff H = 24.7 meV, EH = 32.1 meV, and EH2 = 27.1 meV des des for olivine and Ediff H = 44 meV, EH = 56.7 meV, and EH2 = 46.7 meV for amorphous carbon. In their model they allow for molecules to remain on the surface after formation; 33% and 41% of molecules stay on the surface of olivine and amorphous carbon, respectively. From the analysis of the experiments, they concluded that diffusion of H was slow and thermally activated. Then they applied rate equations to the problem of finding the efficiency of molecular hydrogen formation on a dust grain in interstellar conditions, i.e. low H flux and steady state conditions. The plot of efficiency vs temperature of the grain that resulted from their calculations shows that the molecular hydrogen formation occurs on grains in a rather restricted temperature range. Perets et al.173,174 used a similar method (to be described below) to obtain the efficiency of molecular hydrogen formation on water ice and amorphous silicate surfaces. The result was that, as the experimental data indicated, formation of H2 on amorphous surfaces is more efficient than on ordered surfaces. Cazaux and Tielens237,238 developed a similar but more complex model in which the surface has both physisorption and chemisorption sites and the particle can diffuse both by thermal hopping and by tunneling. They found that molecular hydrogen formation occurs between two H atoms which are physisorbed on the surface and thermal activated diffusion is important. Therefore, they reached similar conclusions as the ones of Katz et al. but with more parameters. Perets et al.173 used a simple rate equation model dNH∈ dt

= F(1 − NH) − WNH − 2ANH 2

Figure 11. Calculated recombination efficiency of hydrogen at steady state on an amorphous silicate (solid line) and on a polycrystalline silicate (dashed line) vs temperature, using the parameters obtained from the TPD experiments. The H flux is appropriate to the one in diffuse clouds. From Perets et al.174 Reproduced by permission of the AAS.

have a distribution of adsorption sites that is wide enough in energy so as to retain H atoms long enough for atoms to diffuse and reactions to take place. As mentioned before, already at 18 K the residence time is a couple of orders of magnitude shorter than at 15 K for a H atom held in a 500 K adsorption site. But H2 formation is efficient in diffuse regions where grains are at 20 K242 and in PDR regions where grains can be at 50−75 K.243 Continuous-time random-walk MonteCarlo simulations were done on several model surfaces to see how a high efficiency of molecular hydrogen formation could be extended to grain temperature above ∼20 K.244 Iqbal et al. considered both physisorption and chemisorption and diffusion by thermal hopping and tunneling. By including chemisorption sites, they could extend the efficiency of H2 formation to 825 K. They also found that at high temperature rate equations overestimate the formation of molecular hydrogen. Finally they studied how the efficiency of H2 formation is influenced by the roughness of the surface: the range of surface temperature for efficient formation of H2 is extended the most when only physisorption is considered. Rate equations overlook other important aspects of the problem, such as the fact that dust grains have a size distribution and that, given the flux of H atoms in typical ISM environments, few H atoms are present at any given time on the smallest grains. Thus, stochastic effects in the formation of molecular hydrogen are important. Lohmar et al.193 modified the rate equations in order to correct for fluctuations and other finite size effects; they were able to obtain accurate results with a simple expression for the rate coefficient. Biham et al.245 and independently Green et al.246 implemented the master equation formalism to adequately describe the population of H atoms on grains. However, the method might not be economically viable since a large number of equations need to be solved. Lipshtat and Biham247,192 compared the production rate of molecular hydrogen on a grain as a function of the number of sites on the grain (which is related to its size) using rate equations, the master equation and the moments equations. It is found that for small grains, with less than about 104 sites, the rate equation overcounts the number of H2 molecules formed on the grain. Next they considered a volume of a cloud and took into account the grain size distribution (assumed to be ∝r−3); per unit volume, small grains are more numerous and thus have an

(8)

where NH is the number of H atoms on the surface, F = nHvHσξ is the flux of atoms impinging and sticking on the surface (σ is the cross section of the grain, ξ is the sticking coefficient and the term 1 − NH is the Langmuir−Hinshelwood rejection term), W = v0 exp[−EH/kBT] is the desorption rate of atoms, and EH is the activation energy for H desorption. A = v0 exp[−Ediff/kBT] is the term that accounts for the depletion of H atoms due to the diffusion-mediated recombination of H into H2 molecules. ν0 is a typical frequency of the particle in the potential energy well, usually taken to be ∼1012 s−1. From comparison with experimental data, one obtains the activation energies for the most important processes; see Table 1 and references cited therein. See Figure 11. The use of the MonteCarlo technique affords to look at more realistic representation of the surface of the grain. For example, different adsorption sites or energy barriers for diffusion can be introduced depending on the morphology of the surface.140,239−241 Given that the message from experiments is that H adsorbs lightly on the surfaces of the analogs investigated, except for H-loaded amorphous carbon or graphite where the Eley−Rideal process takes place between an incoming atom and a chemisorbed atom, it is necessary to 8777


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surface of graphite if H can overcome an entrance energy barrier to the chemisorbed state. This yields H2 formation on an extended surface temperature range. However, so far this has been shown to be true only for graphite and similar surfaces; we still do not have similar results for other allotropic forms of carbon or for silicates which, after all, constitute a large fraction of grains in the ISM. •The ro-vibrational states of molecular hydrogen coming off the surface need to be further characterized, especially for H2 formation on silicates. •There is a need to measure the translational energy of rovibrationally hot molecules. This will be a good aid to guide observations. This will hopefully constrain the way the energy is partitioned between the solid and the newly formed molecule, a still poorly understood aspect of molecule formation at surfaces. •Related to the point above is to assess to what extent the data of the translational and ro-vibrational energy of H2 emerging from a surface is influenced by the size of the sample. Samples used in experiments are necessarily macroscopic, while actual grains are microscopic. One could argue that amorphous or highly disordered surfaces could be considered, as the flow of energy is concerned, approximation of individual microscopic grains, but a theoretical or experimental study to show this would be welcome. •We need more work on efficiency of H2 formation on carbonaceous surfaces, including PAHs over a wide range of dust grain temperature. Only then we will able to asses the relative importance of various surfaces of dust analogs in the formation of H2 in space. •The study of many processes linked to the formation of molecular hydrogen, such as H sticking, H diffusion, isotopic effects, effect of morphology, H and H2 desorption, to name a few, needs to be pursued further. Knowledge of these processes helps constrain models of chemical evolution of clouds and aids theoretical calculations and simulations.

overall larger surface area than larger grains. However, small grains are more inefficient in H2 formation than large grains because there are few H atoms on an individual small grain at any given time. Large grains are more efficient but, when considered in a distribution of sizes, have an overall smaller area. They found that there is a maximum of efficiency for grains with r ≈ 20 nm. The next step is to use there results in a simulation of H2 formation in an ISM environment. Le Petit et al.248 applied the results of the moments equations to the formation of molecular hydrogen in PDRs using the Meudon code, a steady state chemical model for the PDRs.249 Using the parameters obtained from experiments of H2 formation on silicates, amorphous carbon, and ices,172−174 they obtained gas-phase and dust-surface formation rates (cm−3 s−1) of H2 using rate equations and the moments equations as a function of visual extinction Av, i.e., as a function of penetration into the cloud. Le Bourlot250 used the Meudon code and considered both Langmuir−Hinshelwood and Eley−Rideal processes. The former explains H2 formation except in cases where significant H evaporation competes with diffusion, as in strongly illuminated PDRs251 where the Eley−Rideal mechanism takes over as the grain temperature rises. In these regions the formation rate is higher than the ”canonical value” of 3 × 10−17 nHn(H) cm3 s−1. Cuppen et al.252 used the continuous-time random-walk MonteCarlo method to simulate the formation of molecular hydrogen in shocked regions where the grains are bare and the kinetic energy of H is high. In the case of graphite grains, the increased kinetic energy of H allows H to stick to chemisorption sites, thus increasing H2 formation over a range of sample temperatures.

5. CHALLENGES Although it might not appear at first sight, we do have now an understanding, incomplete, for sure, of the formation of molecular hydrogen on dust grain analogs (silicates, ices, carbonaceous materials) at low temperature, less than ∼20 K. By “understanding” I mean that we recognize that in most cases on samples at low temperature hydrogen adsorbs weakly and that molecular hydrogen formation occurs via the Langmuir− Hinshelwood mechanism. On graphite/PAHs, the kinetic energy of the H atoms plays a role, since it can overcome barriers to chemisorption. We have the efficiency of H2 formation on many types of surfaces. We know that the hydrogen molecules that leave the surface after formation are vibrationally hot but less so rotationally. Experiments of H2 formation on ices show that the translational energy is thermal; experiments on silicates and HOPG can only say that the translational energy of emerging H2 is about 1 eV or less.96,97,101,198,199,201,213,253 The OPR of H2 and D2 molecules just formed on surfaces of ices and silicates is the high temperature limit, 3 and 2, respectively. We also know how to translate theoretical and experimental results into simulations of H2 formation on actual dust grains in space environments. There are significant lacunae in our understanding on how molecular hydrogen is formed in space: •Much work has been done on the formation of H2 on water ice, or in simulated ISM environments where hydrogen had already been converted into H2. The real problem of astrophysical interest is to understand how molecular hydrogen forms on analogs of dust grains at “high” temperature (20 < T < 100): this is perhaps the most important unanswered question. Numerous calculations now show that H can chemisorb on the

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work is supported in part by the NSF, Astronomy & Astrophysics Division (Grant No. 0908108) and NASA (Grant No. NNX12AF38G). REFERENCES (1) Bisschop, S. E.; Jørgensen, J. K.; Van Dishoeck, E. F.; De Wachter, E. B. M. Astron. Astrophys. 2007, 465, 913. (2) Nomura, H.; Walsh, C.; Heinzeller, D.; Millar, T. J. EAS Publ. Ser. 2011, 52, 229. (3) Bottinelli, S.; Ceccarelli, C.; Neri, R.; Williams, J. P.; Caux, E.; Cazaux, S.; Lefloch, B.; Maret, S.; Tielens, A. Astrophys. J. Lett. 2004, 617, L69. (4) van Dishoeck, E. Proc. Natl. Acad. Sci., U.S.A. 2006, 103, 12249. (5) Visser, R.; van Dishoeck, E. F.; Doty, S.; Dullemond, C. Astron. Astrophys. 2009, 495, 881. (6) Eddington, A. S. Observatory 1937, 60, 99. (7) Carruthers, G. R. Astrophys. J. 1970, 161, L81. (8) Duley, W.; Williams, D. Interstellar Chemistry; Academic Press: Orlando, FL, 1984. 8778


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