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The chemical network governing interstellar sulfur has been the topic of unrelenting discussion for the past decades due to the conspicuous discrepancy between its expected and observed abundances in different interstellar environments. More recently, the astronomical detections of CH3CH2SH and CH2CS highlighted the importance of interstellar formation routes for sulfur-bearing organic molecules with two carbon atoms. In this work, we perform a laboratory investigation of the solid-state chemistry resulting from the interaction between C2H2 molecules and SH radicals -- both thought to be present in interstellar icy mantles -- at 10 K. Reflection absorption infrared spectroscopy and quadrupole mass spectrometry combined with temperature-programmed desorption experiments are employed as analytical techniques. We confirm that SH radicals can kick-start a sulfur reaction network under interstellar cloud conditions and identify at least six sulfurated products: CH3CH2SH, CH2CHSH, HSCH2CH2SH, H2S2, and tentatively CH3CHS and CH2CS. Complementarily, we utilize computational calculations to pinpoint the reaction routes that play a role in the chemical network behind our experimental results. The main sulfur-bearing organic molecule formed under our experimental conditions is CH3CH2SH and its formation yield increases with the ratios of H to other reactants. It serves as a sink to the sulfur budget within the network, being formed at the expense of the other unsaturated products. The astrophysical implications of the chemical network proposed here are discussed., Comment: 9 figures, 2 pages, Accepted for publication in ACS Earth and Space Chemistry on July 5th 2024

We report the detection of the lowest energy conformer of $E$-1-cyano-1,3-butadiene ($E$-1-C$_4$H$_5$CN), a linear isomer of pyridine, using the fourth data reduction of the GOTHAM deep spectral survey toward TMC-1 with the 100 m Green Bank Telescope. We performed velocity stacking and matched filter analyses using Markov chain Monte Carlo simulations and find evidence for the presence of this molecule at the 5.1$\sigma$ level. We derive a total column density of $3.8^{+1.0}_{-0.9}\times 10^{10}$ cm$^{-2}$, which is predominantly found toward two of the four velocity components we observe toward TMC-1. We use this molecule as a proxy for constraining the gas-phase abundance of the apolar hydrocarbon 1,3-butadiene. Based on the three-phase astrochemical modeling code NAUTILUS and an expanded chemical network, our model underestimates the abundance of cyano-1,3-butadiene by a factor of 19, with a peak column density of $2.34 \times 10^{10}\ \mathrm{cm}^{-2}$ for 1,3-butadiene. Compared to the modeling results obtained in previous GOTHAM analyses, the abundance of 1,3-butadiene is increased by about two orders of magnitude. Despite this increase, the modeled abundances of aromatic species do not appear to change and remain underestimated by 1--4 orders of magnitude. Meanwhile, the abundances of the five-membered ring molecules increase proportionally with 1,3-butadiene by two orders of magnitudes. We discuss implications for bottom-up formation routes to aromatic and polycyclic aromatic molecules.

The impact of including the reactions of C and CH with molecular hydrogen in a gas-grain network is assessed via a sensitivity analysis. To this end, we vary 3 parameters, namely, the efficiency for the reaction \ce{C + H2 -> CH2}, and the cosmic ray ionisation rate, with the third parameter being the final density of the collapsing dark cloud. A grid of 12 models is run to investigate the effect of all parameters on the final molecular abundances of the chemical network. We find that including reactions with molecular hydrogen alters the hydrogen economy of the network; since some species are hydrogenated by molecular hydrogen, atomic hydrogen is freed up. The abundances of simple molecules produced from hydrogenation, such as \ce{CH4}, \ce{CH3OH} and \ce{NH3}, increase, and at the same time, more complex species such as glycine and its precursors see a significant decrease in their final abundances. We find that the precursors of glycine are being preferentially hydrogenated, and therefore glycine itself is produced less efficiently., Comment: 11 pages, 3 figures, accepted for publication in MNRAS

The successive addition of H atoms to CO in the solid phase has been hitherto regarded as the primary route to form methanol in dark molecular clouds. However, recent Monte Carlo simulations of interstellar ices alternatively suggested the radical-molecule H-atom abstraction reaction CH3O + H2CO -> CH3OH + HCO, in addition to CH3O + H -> CH3OH, as a very promising and possibly dominating (70 - 90 %) final step to form CH3OH in those environments. Here, we compare the contributions of these two steps leading to methanol by experimentally investigating hydrogenation reactions on H2CO and D2CO ices, which ensures comparable starting points between the two scenarios. The experiments are performed under ultrahigh vacuum conditions and astronomically relevant temperatures, with H:H2CO (or D2CO) flux ratios of 10:1 and 30:1. The radical-molecule route in the partially deuterated scenario, CHD2O + D2CO -> CHD2OD + DCO, is significantly hampered by the isotope effect in the D-abstraction process, and can thus be used as an artifice to probe the efficiency of this step. We observe a significantly smaller yield of D2CO + H products in comparison to H2CO + H, implying that the CH3O-induced abstraction route must play an important role in the formation of methanol in interstellar ices. Reflection-Absorption InfraRed Spectroscopy (RAIRS) and Temperature Programmed Desorption-Quadrupole Mass Spectrometry (TPD-QMS) analyses are used to quantify the species in the ice. Both analytical techniques indicate constant contributions of ~80 % for the abstraction route in the 10 - 16 K interval, which agrees well with the Monte Carlo conclusions. Additional H2CO + D experiments confirm these conclusions., Comment: 10 pages, 1 table, 6 figures. Accepted in the Astrophysical Journal Letters

Methoxymethanol (CH3OCH2OH, MM) has been identified through gas-phase signatures in both high- and low-mass star-forming regions. This molecule is expected to form upon hydrogen addition and abstraction reactions in CO-rich ice through radical recombination of CO hydrogenation products. The goal of this work is to investigate experimentally and theoretically the most likely solid-state MM reaction channel -- the recombination of CH2OH and CH3O radicals -- for dark interstellar cloud conditions and to compare the formation efficiency with that of other species that were shown to form along the CO-hydrogenation line. Hydrogen atoms and CO or H2CO molecules are co-deposited on top of the predeposited H2O ice to mimic the conditions associated with the beginning of 'rapid' CO freeze-out. Quadrupole mass spectrometry is used to analyze the gas-phase COM composition following a temperature programmed desorption. Monte Carlo simulations are used for an astrochemical model comparing the MM formation efficiency with that of other COMs. Unambiguous detection of newly formed MM has been possible both in CO+H and H2CO+H experiments. The resulting abundance of MM with respect to CH3OH is about 0.05, which is about 6 times less than the value observed toward NGC 6334I and about 3 times less than the value reported for IRAS 16293B. The results of astrochemical simulations predict a similar value for the MM abundance with respect to CH3OH factors ranging between 0.06 to 0.03. We find that MM is formed by co-deposition of CO and H2CO with H atoms through the recombination of CH2OH and CH3O radicals. In both the experimental and modeling studies, the efficiency of this channel alone is not sufficient to explain the observed abundance of MM. These results indicate an incomplete knowledge of the reaction network or the presence of alternative solid-state or gas-phase formation mechanisms., Comment: 8 pages, 8 figures

Simple and complex organic molecules (COMs) are observed along different phases of star and planet formation and have been successfully identified in prestellar environments such as dark and translucent clouds. Yet the picture of organic molecule formation at those earliest stages of star formation is not complete and an important reason is the lack of specific laboratory experiments that simulate carbon atom addition reactions on icy surfaces of interstellar grains. Here we present experiments in which CO molecules as well as C- and H-atoms are co-deposited with H$_2$O molecules on a 10 K surface mimicking the ongoing formation of an "H$_2$O-rich" ice mantle. To simulate the effect of impacting C-atoms and resulting surface reactions with ice components, a specialized C-atom beam source is used, implemented on SURFRESIDE$^3$, an UHV cryogenic setup. Formation of ketene (CH$_2$CO) in the solid state is observed "in situ" by means of reflection absorption IR spectroscopy. C$^1$$^8$O and D isotope labelled experiments are performed to further validate the formation of ketene. Data analysis supports that CH$_2$CO is formed through C-atom addition to a CO-molecule, followed by successive hydrogenation transferring the formed :CCO into ketene. Efficient formation of ketene is in line with the absence of an activation barrier in C+CO reaction reported in the literature. We also discuss and provide experimental evidence for the formation of acetaldehyde (CH$_3$CHO) and possible formation of ethanol (CH$_3$CH$_2$OH), two COM derivatives of CH$_2$CO hydrogenation. The underlying reaction network is presented and the astrochemical implications of the derived pathways are discussed., Comment: Accepted by ApJ

We report new computational and experimental evidence of an efficient and astrochemically relevant formation route to formaldehyde (H$_2$CO). This simplest carbonylic compound is central to the formation of complex organics in cold interstellar clouds, and is generally regarded to be formed by the hydrogenation of solid-state carbon monoxide. We demonstrate H$_2$CO formation via the reaction of carbon atoms with amorphous solid water. Crucial to our proposed mechanism is a concerted proton transfer catalyzed by the water hydrogen bonding network. Consequently, the reactions $^3$C + H$_2$O -> $^3$HCOH and $^1$HCOH -> $^1$H$_2$CO can take place with low or without barriers, contrary to the high-barrier traditional internal hydrogen migration. These low barriers or absence thereof explain the very small kinetic isotope effect in our experiments when comparing the formation of H$_2$CO to D$_2$CO. Our results reconcile the disagreement found in the literature on the reaction route: C + H$_2$O -> H$_2$CO., Comment: Accepted for publication in JPCL

Methane is typically thought to be formed in the solid state on the surface of cold interstellar icy grain mantles via the successive atomic hydrogenation of a carbon atom. In the current work we investigate the potential role of molecular hydrogen in the CH$_4$ reaction network. We make use of an ultra-high vacuum cryogenic setup combining an atomic carbon atom beam and both atomic and/or molecular beams of hydrogen and deuterium on a H$_2$O ice. These experiments lead to the formation of methane isotopologues detected in situ through reflection absorption infrared spectroscopy. Most notably, CH$_4$ is formed in an experiment combining C atoms with H$_2$ on amorphous solid water, albeit slower than in experiments with H atoms present. Furthermore, CH$_2$D$_2$ is detected in an experiment of C atoms with H$_2$ and D$_2$ on H$_2$O ice. CD$_4$, however, is only formed when D atoms are present in the experiment. These findings have been rationalized by means of computational chemical insights. This leads to the following conclusions: a) the reaction C + H$_2$ -> CH$_2$ can take place, although not barrierless in the presence of water, b) the reaction CH + H$_2$ -> CH$_3$ is barrierless, but has not yet been included in astrochemical models, c) the reactions CH$_2$ + H$_2$ -> CH$_3$ + H and CH$_3$ + H$_2$ -> CH$_4$ + H can take place only via a tunneling mechanism and d) molecular hydrogen possibly plays a more important role in the solid-state formation of methane than assumed so far., Comment: Submitted to ApJ

In this work, we reexamine sulfur chemistry occurring on and in the ice mantles of interstellar dust grains, and report the effects of two new modifications to standard astrochemical models; namely, (a) the incorporation of cosmic ray-driven radiation chemistry and (b) the assumption of fast, non-diffusive reactions for key radicals in the bulk. Results from our models of dense molecular clouds show that these changes can have a profound influence on the abundances of sulfur-bearing species in ice mantles, including a reduction in the abundance of solid-phase H$_2$S and HS, and a significant increase in the abundances of OCS, SO$_2$, as well as pure allotropes of sulfur, especially S$_8$. These pure-sulfur species - though nearly impossible to observe directly - have long been speculated to be potential sulfur reservoirs and our results represent possibly the most accurate estimates yet of their abundances in the dense ISM. Moreover, the results of these updated models are found to be in good agreement with available observational data. Finally, we examine the implications of our findings with regard to the as-yet-unknown sulfur reservoir thought to exist in dense interstellar environments., Comment: ApJ, accepted: 37 pages, 8 figures

The radicals HCO and CH$_3$ on carbon monoxide ice surfaces were simulated using density functional theory. Their binding energy on amorphous CO ice shows broad distributions, with approximative average values of 500 K for HCO and 200 K for CH$_3$. If they are located on the surface close to each other (3 to 4 \AA), molecular dynamics calculations based on density functional theory show that they can form acetaldehyde (CH$_3$CHO) or CH$_4$ + CO in barrier-less reactions, depending on the initial orientation of the molecules with respect to each other. In some orientations, no spontaneous reactions were found, the products remained bound to the surface. Sufficient configurational sampling, inclusion of the vibrational zero point energy, and a thorough benchmark of the applied electronic structure method are important to predict reliable binding energies for such weakly interacting systems. From these results it is clear that complex organic molecules, like acetaldehyde, can be formed by recombination reactions of radicals on CO surfaces., Comment: Accepted in ACS Earth and Space Chemistry

The hydrogen abstraction reaction between H and H$_2$S, yielding HS and H$_2$ as products, has been studied within the framework of interstellar surface chemistry. High-temperature rate constants up to 2000 K are calculated in the gas phase and are in agreement with previously reported values. Subsequently low-temperature rate constants down to 55 K are presented for the first time that are of interest to astrochemistry, i.e., covering both bimolecular and unimolecular reaction mechanisms. For this, a so-called implicit surface model is used. Strictly speaking, this is a structural gas-phase model in which the restriction of the rotation in the solid state is taken into account. The calculated kinetic isotope effects are explained in terms of difference in activation and delocalization. All rate constants are calculated at the UCCSD(T)-F12/cc-VTZ-F12 level of theory. Finally, we show that the energetics of the reaction is only affected to a small extent by the presence of H$_2$O or H$_2$S molecular clusters that simulate an ice surface, calculated at the MPWB1K/def2-TZVP level of theory., Comment: Accepted for publication in Journal of Physical Chemistry A http://pubs.acs.org/doi/pdfplus/10.1021/acs.jpca.7b10296

OH radicals play a key role as an intermediate in the water formation chemistry of the interstellar medium. For example the reaction of OH radicals with H$_2$ molecules is among the final steps in the astrochemical reaction network starting from O, O$_2$, and O$_3$. Experimentally it was shown that even at 10 K this reaction occurs on ice surfaces. As the reaction has a high activation energy only atom tunneling can explain such experimental findings. In this study we calculated reaction rate constants for the title reaction on a water-ice I$_h$ surface. To our knowledge, low-temperature rate constants on a surface are not available in the literature. All surface calculations were done using a QM/MM framework (BHLYP/TIP3P) after a thorough benchmark of different density functionals and basis sets to highly accurate correlation methods. Reaction rate constants are obtained using instanton theory which takes atom tunneling into account inherently, with constants down to 110 K for the Eley-Rideal mechanism and down to 60 K for the Langmuir-Hinshelwood mechanism. We found that the reaction is nearly temperature independent below 80 K. We give kinetic isotope effects for all possible deuteration patterns for both reaction mechanisms. For the implementation in astrochemical networks, we also give fit parameters to a modified Arrhenius equation. Finally, several different binding sites and binding energies of OH radicals on the I$_h$ surface are discussed and the corresponding rate constants are compared to the gas-phase case., Comment: Published online. Supporting information on http://pubs.acs.org/doi/suppl/10.1021/acsearthspacechem.7b00052

On the surface of icy dust grains in the dense regions of the interstellar medium a rich chemistry can take place. Due to the low temperature, reactions that proceed via a barrier can only take place through tunneling. The reaction H + H$_2$O$_2$ $\rightarrow$ H$_2$O + OH is such a case with a gas-phase barrier of $\sim$26.5 kJ/mol. Still the reaction is known to be involved in water formation on interstellar grains. Here, we investigate the influence of a water ice surface and of bulk ice on the reaction rate constant. Rate constants are calculated using instanton theory down to 74 K. The ice is taken into account via multiscale modeling, describing the reactants and the direct surrounding at the quantum mechanical level with density functional theory (DFT), while the rest of the ice is modeled on the molecular mechanical level with a force field. We find that H$_2$O$_2$ binding energies cannot be captured by a single value, but rather depend on the number of hydrogen bonds with surface molecules. In highly amorphous surroundings the binding site can block the routes of attack and impede the reaction. Furthermore, the activation energies do not correlate with the binding energies of the same sites. The unimolecular rate constants related to the Langmuir-Hinshelwood mechanism increase as the activation energy decreases. Thus, we provide a lower limit for the rate constant and argue that rate constants can have values up to two order of magnitude larger than this limit., Comment: Accepted for publication in ApJ

This study focuses on the formation of two molecules of astrobiological importance - glycolaldehyde (HC(O)CH2OH) and ethylene glycol (H2C(OH)CH2OH) - by surface hydrogenation of CO molecules. Our experiments aim at simulating the CO freeze-out stage in interstellar dark cloud regions, well before thermal and energetic processing become dominant. It is shown that along with the formation of H2CO and CH3OH - two well established products of CO hydrogenation - also molecules with more than one carbon atom form. The key step in this process is believed to be the recombination of two HCO radicals followed by the formation of a C-C bond. The experimentally established reaction pathways are implemented into a continuous-time random-walk Monte Carlo model, previously used to model the formation of CH3OH on astrochemical time-scales, to study their impact on the solid-state abundances in dense interstellar clouds of glycolaldehyde and ethylene glycol.

Solid state astrochemical reaction pathways have the potential to link the formation of small nitrogen-bearing species, like NH3 and HNCO, and prebiotic molecules, specifically amino acids. To date, the chemical origin of such small nitrogen containing species is still not well understood, despite the fact that ammonia is an abundant constituent of interstellar ices toward young stellar objects and quiescent molecular clouds. This is mainly because of the lack of dedicated laboratory studies. The aim of the present work is to experimentally investigate the formation routes of NH3 and HNCO through non-energetic surface reactions in interstellar ice analogues under fully controlled laboratory conditions and at astrochemically relevant temperatures. This study focuses on the formation of NH3 and HNCO in CO-rich (non-polar) interstellar ices that simulate the CO freeze-out stage in dark interstellar cloud regions, well before thermal and energetic processing start to become relevant. We demonstrate and discuss the surface formation of solid HNCO through the interaction of CO molecules with NH radicals - one of the intermediates in the formation of solid NH3 upon sequential hydrogenation of N atoms. The importance of HNCO for astrobiology is discussed.

Hydroxylamine (NH2OH) is one of the potential precursors of complex pre-biotic species in space. Here we present a detailed experimental study of hydroxylamine formation through nitric oxide (NO) surface hydrogenation for astronomically relevant conditions. The aim of this work is to investigate hydroxylamine formation efficiencies in polar (water-rich) and non-polar (carbon monoxide-rich) interstellar ice analogues. A complex reaction network involving both final (N2O, NH2OH) and intermediate (HNO, NH2O, etc.) products is discussed. The main conclusion is that hydroxylamine formation takes place via a fast and barrierless mechanism and it is found to be even more abundantly formed in a water-rich environment at lower temperatures. In parallel, we experimentally verify the non-formation of hydroxylamine upon UV photolysis of NO ice at cryogenic temperatures as well as the non-detection of NC- and NCO-bond bearing species after UV processing of NO in carbon monoxide-rich ices. Our results are implemented into an astrochemical reaction model, which shows that NH2OH is abundant in the solid phase under dark molecular cloud conditions. Once NH2OH desorbs from the ice grains, it becomes available to form more complex species (e.g., glycine and beta-alanine) in gas phase reaction schemes.

We present a combined experimental and theoretical study focussing on the quantum tunneling of atoms in the reaction between CH4 and OH. The importance of this reaction pathway is derived by investigating isotope substituted analogs. Quantitative reaction rates needed for astrochemical models at low temperature are currently unavailable both in the solid state and in the gas phase. Here, we study tunneling effects upon hydrogen abstraction in CH4 + OH by focusing on two reactions: CH4 + OD -> CH3 + HDO and CD4 + OH -> CD3 + HDO. The experimental study shows that the solid-state reaction rate R(CH4 + OD) is higher than R(CD4 + OH) at 15 K. Experimental results are accompanied by calculations of the corresponding unimolecular and bimolecular reaction rate constants using instanton theory taking into account surface effects. From the work presented here, the unimolecular reactions are particularly interesting as these provide insight into reactions following a Langmuir-Hinshelwood process. The resulting ratio of the rate constants shows that the H abstraction (k(CH4 + OD)) is approximately ten times faster than D-abstraction (k(CD4 + OH)) at 65 K. We conclude that tunneling is involved at low temperatures in the abstraction reactions studied here. The unimolecular rate constants can be used by the modeling community as a first approach to describe OH-mediated abstraction reactions in the solid phase. For this reason we provide fits of our calculated rate constants that allow the inclusion of these reactions in models in a straightforward fashion., Comment: Accepted by A&A

The final step of the water formation network on interstellar grain surfaces starting from the H + O$_2$ route is the reaction between H and H$_2$O$_2$. This reaction is known to have a high activation energy and therefore at low temperatures it can only proceed via tunneling. To date, however, no rate constants are available at temperatures below 200 K. In this work, we use instanton theory to compute rate constants for the title reaction with and without isotopic substitutions down to temperatures of 50 K. The calculations are based on density functional theory, with additional benchmarks for the activation energy using unrestricted single-reference and multireference coupled-cluster single-point energies. Gas-phase bimolecular rate constants are calculated and compared with available experimental data not only for H + H$_2$O$_2$ $\rightarrow$ H$_2$O + OH, but also for H + H$_2$O$_2$ $\rightarrow$ H$_2$ + HO$_2$. We find a branching ratio where the title reaction is favored by at least two orders of magnitude at 114 K. In the interstellar medium this reaction predominantly occurs on water surfaces, which increases the probability that the two reactants meet. To mimic this one, two, or three spectator H2O molecules are added to the system. Eley-Rideal bimolecular and Langmuir-Hinshelwood unimolecular rate constants are presented here. The kinetic isotope effects for the various cases are compared to experimental data as well as to expressions commonly used in astrochemical models. Both the rectangular barrier and the Eckart approximations lead to errors of about an order of magnitude. Finally, fits of the rate constants are provided as input for astrochemical models., Comment: Accepted for publication by Phys. Chem. Chem. Phys. 2016. Supplementary information available: http://www.rsc.org/suppdata/c6/cp/c6cp06457d/c6cp06457d1.pdf

We have investigated the thermally induced proton/deuteron exchange in mixed amorphous H$_2$O:D$_2$O ices by monitoring the change in intensity of characteristic vibrational bending modes of H$_2$O, HDO, and D$_2$O with time and as function of temperature. The experiments have been performed using an ultra-high vacuum setup equipped with an infrared spectrometer that is used to investigate the spectral evolution of homogeneously mixed ice upon co-deposition in thin films, for temperatures in the 90 to 140 K domain. With this non-energetic detection method we find a significantly lower activation energy for H/D exchange -- $3840 \pm 125$ K -- than previously reported. Very likely this is due to the amorphous nature of the interstellar ice analogues involved. This provides reactive timescales ($\tau<10^4$ years at $T$ $>70$ K) fast enough for the process to be important in interstellar environments. Consequently, an astronomical detection of D$_2$O will be even more challenging because of its potential to react with H$_2$O to form HDO. Furthermore, additional experiments, along with previous studies, show that proton/deuteron swapping also occurs in ice mixtures of water with other hydrogen bonded molecules, in particular on the OH and NH moieties. We conclude that H/D exchange in ices is a more general process that should be incorporated into ice models that are applied to protoplanetary disks or to simulate the warming up of cometary ices in their passage of the perihelion, to examine the extent of its influence on the final deuteron over hydrogen ratio., Comment: 10 pages, 8 figures, accepted for publication in MNRAS

The formation of interstellar water has been commonly accepted to occur on the surfaces of icy dust grains in dark molecular clouds at low temperatures (10-20 K), involving hydrogenation reactions of oxygen allotropes. As a result of the large abundances of molecular hydrogen and atomic oxygen in these regions, the reaction H2 + O has been proposed to contribute significantly to the formation of water as well. However, gas phase experiments and calculations, as well as solid-phase experimental work contradict this hypothesis. Here, we use precisely executed temperature programmed desorption (TPD) experiments in an ultra-high vacuum setup combined with kinetic Monte Carlo simulations to establish an upper limit of the water production starting from H2 and O. These reactants are brought together in a matrix of CO2 in a series of (control) experiments at different temperatures and with different isotopological compositions. The amount of water detected with the quadrupole mass spectrometer upon TPD is found to originate mainly from contamination in the chamber itself. However, if water is produced in small quantities on the surface through H2 + O, this can only be explained by a combined classical and tunneled reaction mechanism. An absolutely conservative upper limit for the reaction rate is derived with a microscopic kinetic Monte Carlo model that converts the upper limit into a maximal possible reaction rate. Incorporating this rate into simulations run for astrochemically relevant parameters, shows that the upper limit to the contribution of the reaction H2 + O in OH, and hence water formation, is 11% in dense interstellar clouds. Our combined experimental and theoretical results indicate however, that this contribution is likely to be much lower., Comment: 9 pages, 4 figures