Attachment of Water and Alcohol Molecules onto Water and Alcohol

Article pubs.acs.org/JPCA

Attachment of Water and Alcohol Molecules onto Water and Alcohol Clusters Isabelle Braud, Julien Boulon, Sébastien Zamith, and Jean-Marc L’Hermite* Laboratoire Collisions Agrégats Réactivité, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse, France CNRS, UMR 5589, F-31062 Toulouse, France S Supporting Information *

ABSTRACT: Absolute attachment cross sections of single molecules M (M = water, ethanol, or methanol) onto positively charged mass-selected clusters XnH+ (X = water, ethanol, or methanol) were measured for cluster sizes ranging from tens to hundreds of molecules and center-of-mass collision energies varying from 0.1 to ∼1 eV. The attachment cross sections, which converge as expected toward geometrical cross sections at large cluster sizes, are systematically and noticeably lower than geometrical cross sections at small sizes. Attachment cross sections depend barely on the nature of the reactants. Homogeneous attachment reactions XnH+ + X → Xn+1H+ can be accounted for by a dynamical collisional model, in which the intermolecular interactions between the target cluster and the impinging molecule can be neglected. Dynamical arguments account satisfactorily for size and energy dependences of attachment cross sections and also for their variation from one element to another. It is thus suggested that either the attachment probabilities are likely to be more governed by the capacity of clusters to absorb collision energy rather than by cluster/molecule intermolecular interactions, or it indicates that the strength of these interactions does not differ noticeably among the hydrogen-bonded systems investigated. However, for inhomogeneous reactions of the form XnH+ + Y → XnYH+ (X, Y = water, ethanol, methanol), although the global size dependences are qualitatively reproduced, the variations of attachment cross sections with the nature on the impinging molecule are not satisfactorily accounted for within the simple empirical model proposed for homogeneous reactions.

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INTRODUCTION Water, ethanol, and methanol are important solvent molecules involved in many chemical and physical processes. From the beginning of clusters studies in molecular beams, small isolated clusters of these three compounds were investigated1 owing to the fascinating structural properties of their highly directional hydrogen bonds. The study of water interactions with volatile organic compounds such as methanol (MeOH) and ethanol (EtOH) is also of high interest in atmospheric physics, where they may play a role as nucleation seeds.2 In the collisions of single molecules onto clusters, the intermolecular forces are expected to affect the probability for the cluster to accommodate an additional impinging molecule. Above a certain size range, however, the interaction range of the intermolecular forces becomes negligible with respect to the size of particles, and the cross section converges asymptotically toward geometrical, that is, hard-sphere, cross sections. Below this asymptotic limit and as far as the molecular interactions between clusters and molecules are attractive, unimolecular attachment cross sections are expected to be larger than geometrical cross sections. However, assuming that no thermal evaporation occurs within the observation time, it had already been shown that attachment cross sections may be lower than hard-sphere cross sections. The attachment cross sections of water molecules onto protonated and deprotonated water clusters are significantly lower than geometrical cross sections.3−5 These lower than expected attachment proba© 2015 American Chemical Society

bilities were ascribed to a reduced capacity for the target to absorb collision energy when the interaction time between the target and the projectile is too short. In order to put to the test this speculative interpretation, attachment reactions are studied using different molecular projectiles and cluster targets, namely, water, ethanol, and methanol. The intermolecular interactions in ethanol and methanol clusters are dominated, as water clusters, by hydrogen bonding.1,6−11 In a collision model previously applied to water clusters,3 the conversion of the kinetic energy of the impinging molecule into internal energy of the cluster was assumed to depend on the efficiency of the cluster’s intermolecular surface bending mode’s excitation, which strongly depends on the collision duration. A characteristic time below which the energy transfer is inefficient was extracted from experimental attachment cross sections and proved to be very close to the vibrational period of the main cluster’s excited surface mode.3 As a rule of thumb in the frame of this model, this characteristic time would be expected to increase with the molecular mass of cluster’s molecular units. The present study shows that homogeneous reactions XnH+ + X → Xn+1H+ comply with Special Issue: Jean-Michel Mestdagh Festschrift Received: November 27, 2014 Revised: February 16, 2015 Published: February 17, 2015 6017

DOI: 10.1021/jp511854r J. Phys. Chem. A 2015, 119, 6017−6023

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The Journal of Physical Chemistry A

protonated water clusters, the cluster mass is rigorously M = nm + mH, where mH is the proton mass). In practice, experiments are conducted at constant kinetic energy Ek in the laboratory frame.12 For homogeneous collisions (m = m′) at fixed Ek, the collision energy Ec decreases roughly as 1/n with increasing cluster size n. For inhomogeneous collisions (m′ ≠ m), when collisions at similar collision energies Ec are to be compared, the kinetic energy in the lab frame Ek must be divided by a factor of m/m′ (neglecting the contribution of the thermal motion of the molecular targets). The collision energies achieved in the experiments presented here are on the order of 0.1 eV; for example, for methanol molecules in collision with methanol clusters in the size range n = 40−150 at Ek = 12 eV, the collision energies vary in the range of Ec = 0.12−0.34 eV.

this rule, whereas inhomogeneous attachment reactions XnH+ + Y → XnYH+ do not obey this empirical law. After a brief description of the experimental method employed, we will examine the experimental attachment cross sections obtained for homogeneous attachment reaction where the impinging molecule is the same as the components of the target clusters. These homogeneous reactions involving ethanol and methanol are shown to obey the empirical collision model developed previously for water. In the following section, the attachment cross sections of inhomogeneous reactions will be shown to disagree with this model.

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EXPERIMENTAL METHOD The experimental setup and the method used to measure absolute attachment cross sections of single molecules onto mass-selected clusters was already detailed elsewhere.4 Water, methanol, or ethanol clusters are produced in a gas aggregation source. The clusters are ionized in the source chamber either by a discharge produced by applying a negative voltage to a ring electrode or electron impact. In the last case, a miniature electron gun is placed in the source chamber. After their production, the clusters, seeded in helium carrier gas, are thermalized in a heat bath. The clusters are then mass selected, and their translational kinetic energy can be reduced down to less than 10 eV in the laboratory frame, that is, to a few tenths of an eV in the center-of-mass (CM) frame.4 They enter a collision cell containing a controlled pressure of water, methanol, or ethanol vapor. At the output of the collision cell, the collision products are mass analyzed with a time-offlight mass spectrometer. The corresponding mass spectra contain, besides the peak parent cluster, clusters that have undergone one or several attachment collisions. The attachment cross sections are deduced from these mass spectra detected at the output of the reaction cell using the expression σ=−

νcluster ln(I /I0) νrel ρl

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EXPERIMENTAL RESULTS (1). Getting Rid of Evaporation Spurious Effects. An important issue in our experiments is to make sure that clusters do not evaporate any molecule after they have undergone attachment, which would artificially lower the measured attachment cross sections. This is why in all of the experiments presented here care was taken to ensure that no evaporation occurred after attachment. We first took the precaution of recording the attachment cross sections at a low cluster temperature (typically 30 K) in order to reduce the evaporation probability. Moreover, for several small clusters, the attachment probability was recorded as a function of the cluster’s initial temperature in order to identify the critical temperature from which evaporation starts to occur. The attachment cross sections plotted as a function of the cluster’s initial temperature are shown in Figure 1 for water, methanol, and ethanol clusters. At low temperatures, the attachment cross sections do not vary significantly. Above a given temperature, the cross sections drop due to unimolecular evaporation; after an attachment has occurred, the cluster evaporates the attached molecule before it is detected. In the examples displayed in Figure 1, it is clear that at 30 K (the working temperature in attachment cross section experiments), no evaporation has occurred yet. The temperatures at which the drop in attachment cross sections occurs depend on both cluster size and collision energy. All of the data presented in the paper are measured for collision energy−cluster size couples for which no evaporation occurred. Numerical simulations of the effect of thermal evaporation on the measured cross sections were performed in order to check that thermal evaporation is actually responsible for the underestimation of measured cross sections at high temperature. The calculated curves shown in Figure 1 were obtained by Monte Carlo simulations of the whole trajectories of clusters across all of the electric fields crossed in the experiment from the output of the thermalizer up to the detector, including, of course, attachment events in the collision chamber and all subsequent evaporations. Realistic mass spectra were generated, which were analyzed using the data processing program used to analyze experimental data. These simulations allowed us also to validate the values of the kinetic energies of the clusters. The initial internal energy of clusters iwas statistically distributed according to the canonical distribution at temperature T; the distributions of the cluster’s initial translational velocities and positions were chosen in order to reproduce experimental conditions. Under each attachment collision, the internal energy of a cluster was increased by the binding energy of an

(1)

where vcluster is the cluster velocity in the laboratory frame, ρ is the density in the cell, and l is the effective length of the collision cell. I is the intensity of the peak of the intact parent cluster, and I0 is the total intensity integrated over all peaks. vrel is the average relative velocity given by5 ⎛ 1 e −a ⎞ ⎟ vrel = vcluster ⎜erf( a ) + erf( a ) + ⎝ πa ⎠ 2a

(2)

(m′v2cluster)/(2kBT),

with a = where m′ is the mass of the vapor molecules in the cell. In our experimental setup, the kinetic energy of clusters is controlled in the laboratory frame.12 The collision energy in the CM frame Ec is related to Ek by4 Ec = E k

m′ 3 M + kBT m′ + M 2 m′ + M

(3)

where m′ is the mass of the impinging molecule, M is the cluster mass, kB is the Boltzmann constant, and T is the temperature of the vapor in the collision cell (room temperature). The second term on the right-hand side of eq 3 is the contribution of the thermal motion of molecules in the collision cell. If we denote m as the mass of the molecular units of the cluster and n as the number of molecules in the cluster, the cluster mass M is roughly nm(since we deal here with 6018


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additional molecule, plus the collision energy. Cluster evaporation rates were calculated using the Weisskopf model of unimolecular evaporation presented in the Supporting Information. The calculated attachment cross sections shown in Figure 1 reproduce satisfactorily the experimental data. The parameters of the Weisskopf model of unimolecular evaporation were calibrated on water. The main parameters of this model are the intermolecular vibrational frequencies and the dissociation energies (see the Supporting Information). The vibrational frequency chosen for water clusters was νo = 1.202 × 1012 s−1, and the dissociation energies were taken from ref 13. The dissociation energies chosen for methanol and ethanol were DMethanol = 0.4 eV and DEthanol = 0.42 eV, respectively. These values are very close to the enthalpy of vaporization per molecule deduced from bulk data (0.37 eV/molecule for methanol and 0.4 eV/molecule for ethanol). The vibrational frequencies used for ethanol and methanol were scaled with respect to the one of water under a harmonic approximation under the two following hypothesis. The frequency of classical harmonic oscillator is v = (k/m)1/2, where m is the mass of a cluster molecular unit, and the constant k is considered here to be the same for water, ethanol, and methanol; the dissociation energies of water, ethanol, and methanol clusters being very close to one another allows one to assume that the strengths of intermolecular forces are roughly similar for all of these molecular clusters. Therefore, we chose to scale the vibrational frequencies only as a function of molecular mass vEthanol = vWater × (mWater/mEthanol)1/2 = 0.752 × 1012 s−1 and vMethanol = vWater × (mWater/mMethanol)1/2 = 0.902 × 1012 s−1. Apart from this massscaling of vibrational frequencies and the use of different dissociation energies, the parameters used in the simulations for water, ethanol, and methanol are rigorously identical. The good simulation/experiment agreement under these realistic hypotheses proves that thermal evaporation is likely to be responsible for the shape of the experimental curves shown in Figure 1. Therefore, it indicates that as long as the cluster’s temperature is kept low enough, the measured attachment cross sections are reliable and, in particular, that they do not suffer from any underestimation due to evaporation. In the following, we will first recall the main results concerning the attachment cross sections of water molecules onto protonated water clusters, which were already presented in previous publications3−5 and will be used as reference in the discussions about ethanol and methanol. The unreleased experiments presented in this paper can be partitioned in two categories: homogeneous attachment reactions XnH+ + X, where the impinging molecule is of the same nature as the molecular components of the cluster, and the inhomogeneous reaction XnH+ + Y ≠ X, where they are different. We will examine successively homogeneous reactions and then inhomogeneous ones. (2). Attachment of Water Molecules onto Water Clusters. The analysis of attachment probabilities of water molecules onto water clusters (Figure 2a) showed that the attachment cross sections, which converge toward geometrical cross sections at large cluster sizes, are systematically lower than geometrical cross sections at small sizes.3,4 The ratio of nonsticking collisions increases as the CM collision energy increases as the size decreases. These features cannot merely be accounted for by electrostatic interactions. There is an attractive interaction between charged clusters and neutral molecules due to the interaction between the charge and both

Figure 1. (a) Squares: Experimental attachment cross section of water molecules onto the protonated water cluster (H2O)60H+ plotted as a function of the cluster’s initial temperature, measured at the cluster’s kinetic energy Ek = 33 eV in the laboratory frame. Continuous Line: Monte Carlo numerical simulation calculated with the Weisskopf frequency ν0 = 1.202 × 1012 s−1 and the dissociation energies of protonated water clusters taken from ref 13. (b) Squares: Experimental attachment cross section of methanol molecules onto the protonated methanol cluster (MeOH)50H+ plotted as a function of the cluster’s initial temperature, measured at the constant cluster’s kinetic energy Ek = 22 eV in the laboratory frame. Continuous Line: Monte Carlo numerical simulation calculated with the Weisskopf frequency νmethanol = 0.902 × 1012 s−1 and a size-independent dissociation energy of 0.4 eV. (c) Squares: Experimental attachment cross section of ethanol molecules onto the protonated ethanol cluster (EtOH)40H+ plotted as a function of the cluster’s initial temperature, measured at the constant cluster’s kinetic energy Ek = 22 eV in the laboratory frame. Continuous Line: Monte Carlo numerical simulation calculated with the Weisskopf frequency νethanol = 0.752 × 1012 s−1 and a size-independent dissociation energy of 0.42 eV. 6019


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A proton transfer from the cluster onto the molecule, which would be likely to enhance significantly the attachment cross sections (“harpooning” mechanism14), is not likely to occur because the proton affinity of clusters is larger than the proton affinity of single molecules;15 consequently, apart from steric corrections due to the different sizes of water, methanol, and ethanol molecules, the attachment cross sections are not expected to differ considerably from water to methanol or ethanol. Finally, our observations had shown that some collisions occurring within the geometrical cross section do not lead to attachment, although, as demonstrated in the previous section, no thermal evaporation occurs after the collision. It means that some direct (i.e., in a short time scale with respect to the collision duration) phenomenon prevents the molecules from attaching onto clusters although a head-on collision takes place. It was suggested that the attachment probability of molecules onto clusters may be reduced by a dynamical effect related to the collision time dependence of the cluster’s ability to absorb collision energy.3,4 The main assumption of the empirical model built to account for this effect is that the conversion of collision energy into the cluster’s internal energy is inefficient when the the interaction time between the impinging molecule and the target cluster is short compared to the vibrational period of the water cluster’s surface main vibration mode. If the collision time is too short, the impinging molecule hits the cluster without undergoing attachment. Within this model, the ratio of attachment to geometrical cross sections is given by the following expression3 σexp σgeo

⎛ τ − τ0 ⎞ = 1 − exp⎜ − c ⎟ τv ⎠ ⎝

(4)

where σgeo = π(Rcluster + rmolecule)2 is the geometrical cross section, τv is the vibrational period of the main surface vibrational mode excited through the collision, τ0 is a lag time, and τc is the duration of the collision time approximated by τc = Figure 2. (a) Log−log plot of the water clusters−water molecules attachment cross section as a function of cluster size for five different kinetic energies in the laboratory frame. Experimental results are compared to the hard-sphere model (dotted line). The full lines through the data points are calculated using eq 4 with the parameters rm = 2.4 Å, τv = 0.66 ps, and τ0 = 0.52 ps (reproduced from ref 4). For comparison, the results of Lengyel et al.19 for neutral water clusters are also plotted as open circles. (b) Log−log plot of the protonated methanol clusters−methanol molecules attachment cross section as a function of cluster size for the two kinetic energies in the laboratory frame Ek = 12 (red triangles) and 22 eV (black squares). Experimental results are compared to the hard-sphere model (dashed line). The full lines through the data points are calculated using eq 4. (c) Log−log plot of the protonated ethanol clusters−ethanol molecules attachment cross section as a function of cluster size for the kinetic energies in the laboratory frame Ek = 22 eV. Experimental results (symbols) are compared to the hard-sphere model (dotted line). The full line through the data points is calculated using eq 4.

2n1/3rm vrel

(5)

where n is the number of molecules in the cluster and m and rm are the mass and radius, respectively, of a single molecule. As shown in Figure 2a, the experimental attachment cross sections of water molecules onto protonated water clusters are quite nicely reproduced at several collision energies using eq 4. The most significant parameter in eq 4 is the vibrational time τv associated with the period of the main surface vibrational mode of the cluster excited in the collision.3,4 The characteristic time τv (0.66 ps) deduced from our experiments on water is close to the period of the main low-energy surface vibrational mode excited by collisions of rare gas atoms onto water clusters, the O···O···O bending mode.16,17 The molecular radius deduced from the fit of our experimental curves was recently re-evaluated to 2.4 Å.18 This value is quite higher than the radius deduced from the density of ice (1.98 Å). As stated above, this might be due to the attractive interaction between the charge of the cluster and the permanent dipole of the water molecules. In Figure 2a, we compare our results with a recent experiment by Lengyel et al.19 where they measured the attachment cross section of water molecules onto neutral water clusters. The agreement with our lowest kinetic energy results is

the permanent and induced dipole of the impinging molecules. In the size and collision energy ranges considered here, only a small enhancement of the attachment cross sections with respect to hard-sphere cross sections would be expected due to the attractive interaction between the target and the projectile.4 6020


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vibrational mode should scale, in a harmonic approximation, as √m, where m is the mass of the molecular units. Thus, if τw is the period of the surface intermolecular bending vibrational mode of water clusters, the period of the same mode for methanol and ethanol, τm and τe respectively, is expected to scale approximately as

very good up to sizes of around 250. For larger sizes, Lengyel et al. found that the cross section becomes higher than the geometrical cross section due to irregular shapes of the clusters. The CM collision energy was about 0.2 eV in the experiment by Lengyel et al. In our case, for 6 eV in the laboratory frame, the CM collision energy evolved from 0.23 eV for n = 30 to 0.07 eV for n = 200. The fact that we find compatible values for the cross sections in both experiments despite the different nature of the collisions (neutral−neutral versus charged− neutral) would tend to indicate that the measured cross sections are independent of the electrostatic interactions between the colliders. However, in ref 19, Lengyel et al. were able to reproduce satisfactorily the size dependence of their measured cross section up to sizes of around n = 250 using a spherical cluster model based on the neutral−neutral potential interaction. We are not able at present to explain the apparent contradictions between the interpretation of the results of these experiments. Theoretical calculation of the attachment cross section for collisions of charged water clusters with neutral water molecules based on molecular dynamics simulation would help to interpret our results. (3). Homogeneous Unimolecular Nucleation XnH+ + X → Xn+1H+. The attachment cross sections of methanol molecules onto methanol clusters and of ethanol molecules onto ethanol clusters are shown in Figure 2b and c, respectively. The overall evolution with cluster size of the attachment cross sections is similar to the observations for water. In particular, at small sizes, the attachment cross sections are much lower than geometrical cross sections. In methanol and ethanol clusters, one can reasonably expect, as for water clusters, that the surface intermolecular bending mode is the main vibrationnal mode excited in the collisions. Under the same hypothesis as that for water, eq 4 is parametrized in order to reproduce experimental data. τv and τ0 are the only free parameters; the molecular radii rm used in eq 5 are deduced from the density of bulk solid ethanol (rm = 2.612 Å20) and methanol (rm = 2.337 Å21). A good experiment−model agreement is obtained concerning both the size evolution and energy dependence (for methanol) of the attachment cross sections. The values of τv found for methanol (1.19 ps) and ethanol (1.69 ps) are larger than that for water. No data are available about the surface vibrational modes of ethanol or methanol clusters excited by collisions. However, under reasonable physical assumptions, one can speculate about the evolution of τv from water to methanol and ethanol. We will show below that our experimental data are compatible, within the rough collision model developed for water recalled above, with the expected properties deduced from the mere mass difference between water, ethanol, and methanol. The cohesive energy of methanol and ethanol clusters is expected to be close to the one of water clusters, although probably slightly lower. The intermolecular forces between ethanol and methanol molecules are likely to be mainly due, as for water clusters, to hydrogen bonds. The dissociation energy of methanol clusters is close to 0.3 eV for 12 molecule clusters,6 whereas the dissociation energy of water clusters is around 0.45 eV for 40−100 molecule clusters.13 Thus, the molecular binding energies of ethanol clusters are not expected to be very different than those of methanol. Assuming that the intermolecular forces between water molecules, ethanol, and methanol molecules in clusters are of the same order of magnitude, the period of the surface

τm,e = τw ×

mm,e /m w

(6)

where mw, mm, and me are the molecular masses of water, methanol, and ethanol, respectively. Assuming a surface bending vibrational period of τw = 0.66 ps for water,16,17 the values obtained from eq 6 for methanol and ethanol are τm = 0.88 ps and τe = 1.06 ps, respectively, to be compared to the exp experimental values τexp = 1.69 ps. As m = 1.19 ps and τe expected, the vibrational period increases with molecular mass, which is coherent with the model. The attachment cross sections of methanol molecules onto methanol clusters were measured for two collision energies in the laboratory frame, namely, 12 and 22 eV, over an extended size range (Figure 2b). The two theoretical curves at 12 and 22 eV, respectively, are obtained from eq 4 with the same set of parameters τv = 1.19 ps, rm = 2.337 Å, and τ0 = 0.5 ps. As for water clusters, the model reproduces the collision energy dependence of attachment cross sections. (4). Inhomogeneous Attachment Reactions XnH+ + Y → YXnH+. The attachment cross sections of water, methanol, and ethanol molecules onto water clusters (Figure 3a) and methanol (Figure 3b) clusters were measured at constant collision energy. The kinetic energies of incoming clusters Ek were varied so that the CM collision energy Ec is kept constant for a given cluster mass. The theoretical predictions given by eq 4 are also shown in Figure 3a and b, using the parameters extracted from experiments on homogeneous systems presented above. In these inhomogeneous reactions, the overall features of size and energy dependence of attachment cross sections are similar to those observed for homogeneous reactions; in particular, the cross sections are systematically lower than geometrical cross sections. As for homogeneous attachment, simple electrostatic considerations cannot explain this feature; similarly, the cross sections are not expected to be considerably enhanced by strong attractive interactions. Harpooning reactions are not likely to occur because the proton affinity of impinging molecules is lower than the one of clusters, even in the most favorable case a priori of water clusters−ethanol molecule reactions. Although the proton affinity of the ethanol molecule (8.24 eV22) is higher than the one of the water molecule (∼7.5 eV15,22), the proton affinity of a water dimer (8.96 eV15) is already higher than the one of one ethanol molecule. However, beyond the overall rough theory−experiment agreement concerning the size dependence, eq 4 cannot reproduce satisfactorily our data within experimental uncertainties, contrary to homogeneous attachment reactions. For both (H2O)nH+ and (MeOH)nH+ target clusters, the cross sections are roughly the same for all molecular projectiles at constant collision energy, whereas our model predicts a variation, as shown in Figure 3a and b, because the collision duration varies with the mass of the molecular projectile at constant collision energy. In the frame of the model presented above, when the nature of the impinging molecule varies, the cross sections should be conserved at constant velocity and not at constant collision energy. To conclude, the simple model 6021


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at collision energies in the range of tens of eV are demonstrated to hardly depend on the electrostatic interactions between the impinging molecules and the clusters. A dynamical collision model, which relates the attachment probabilities to the capacity of the cluster to accommodate the collision energy during the collision time, is able to reproduce the main features of homogeneous (i.e., where the cluster units and the impinging molecules are the same) attachment reactions but fails in accounting for inhomogeneous reaction attachment cross sections. Complementary theoretical studies are necessary to disentangle dynamical versus energetic effects in these attachment reactions.

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ASSOCIATED CONTENT

S Supporting Information *

The expression of the evaporation rate used in our Monte Carlo simulations to describe unimolecular evaporation of water clusters is derived. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been partly funded by the Agence Nationale de la Recherche (ANR) under Grant No. ANR 2011-BS04-028-01.

Figure 3. (a) Log−log plot as a function of cluster size of attachment cross sections of methanol (red circles), ethanol (green triangles), and water (black squares) molecules onto protonated water clusters. The collision energies in the laboratory frame are 9, 12, and 22 eV for ethanol, methanol, and water molecules, respectively, in order to keep comparable collision energies in the CM frame from one molecule to another (see the text). Experimental results are compared to the hardsphere model (dotted lines). The full lines through the data points are calculated using eq 4. (b) Log−log plot as a function of cluster size of attachment cross sections of methanol (black squares), ethanol (red circles), and water (green triangles) molecules onto protonated methanol clusters. The collision energies in the laboratory frame are 15, 22, and 38 eV for ethanol, methanol, and water molecules, respectively, in order to keep comparable collision energies in the CM frame from one molecule to another (see the text). Experimental results are compared to the hard-sphere model (dotted lines). The full lines through the data points are calculated using eq 4.

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REFERENCES

(1) Kay, B. D.; Castleman, A. W., Jr. Molecular Beam Electric Deflection Study of the Hydrogen-Bonded Water, Methanol, and Ethanol Clusters (H2O)N, (CH3OH)N, and (C2H5OH)N. J. Phys. Chem. 1985, 89, 4867−4868. (2) Lengyel, J.; KoCisek, J.; Poterya, V.; Pysanenko, A.; SvrCkova, P.; Farnik, M.; Zaouris, D. K.; Fedor, J. Uptake of Atmospheric Molecules by Ice Nanoparticles: Pickup Cross Sections. J. Chem. Phys. 2012, 137, 034304−034307. (3) Zamith, S.; Feiden, P.; Labastie, P.; L’Hermite, J.-M. Sticking Properties of Water Clusters. Phys. Rev. Lett. 2010, 104, 103401−4. (4) Zamith, S.; Feiden, P.; Labastie, P.; L’Hermite, J.-M. Attachment Cross Sections of Protonated Water Clusters. J. Chem. Phys. 2010, 133, 154305−154310. (5) Zamith, S.; de Tournadre, G.; Labastie, P.; L’Hermite, J.-M. Attachment Cross-Sections of Protonated and Deprotonated Water Clusters. J. Chem. Phys. 2013, 138, 034301−034304. (6) Boyd, S. L.; Boyd, R. J. A Density Functional Study of Methanol Clusters. J. Chem. Theory Comput. 2006, 3, 54−61. (7) Buck, U.; Huisken, F. Infrared Spectroscopy of Size-Selected Water and Methanol Clusters. Chem. Rev. 2000, 100, 3863−3890. (8) Hagemeister, F. C.; Gruenloh, C. J.; Zwier, T. S. Density Functional Theory Calculations of the Structures, Binding Energies, and Infrared Spectra of Methanol Clusters. J. Phys. Chem. A 1998, 102, 82−94. (9) Nishi, N.; Koga, K.; Ohshima, C.; Yamamoto, K.; Nagashima, U.; Nagami, K. Molecular Association in Ethanol−Water Mixtures Studied by Mass Spectrometric Analysis of Clusters Generated through Adiabatic Expansion of Liquid Jets. J. Am. Chem. Soc. 1988, 110, 5246−5255. (10) Shi, Y. J.; Consta, S.; Das, A. K.; Mallik, B.; Lacey, D.; Lipson, R. H. A 118 nm Vacuum Ultraviolet Laser/Time-of-Flight Mass Spectroscopic Study of Methanol and Ethanol Clusters in the Vapor Phase. J. Chem. Phys. 2002, 116, 6990−6999.

that leads to eq 4 reproduces satisfactorily the homogeneous attachment cross sections of water, ethanol, and methanol, but it does not account for the experimental results for inhomogeneous reactions XnH+ + Y ≠ X → YXnH+. Lengyel et al. have also reported attachment cross sections of ethanol and methanol molecules onto neutral water clusters containing 260 molecules.2 Their reported values are 670 and 855 Å2 for methanol and ethanol, respectively. The values obtained are compatible with the prediction of our model at large sizes, which is essentially given by the geometrical cross section. However, we do not observe a dependence of the protonated water attachment cross section with the nature of the projectile.

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CONCLUSION The absolute attachment cross sections of water, ethanol, and methanol molecules onto water, ethanol, and methanol clusters 6022


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The Journal of Physical Chemistry A (11) Sum, A. K.; Sandler, S. I. Ab Initio Calculations of Cooperativity Effects on Clusters of Methanol, Ethanol, 1-Propanol, and Methanethiol. J. Phys. Chem. A 2000, 104, 1121−1129. (12) Chirot, F.; Zamith, S.; Labastie, P.; L’Hermite, J.-M. New Device to Study Unimolecular Cluster Nucleation. Rev. Sci. Instrum. 2006, 77, 063108. (13) Hansen, K.; Andersson, P. U.; Uggerud, E. Activation Energies for Evaporation from Protonated and Deprotonated Water Clusters from Mass Spectra. J. Chem. Phys. 2009, 131, 124303−124307. (14) Levine, R. D. Molecular Reaction Dynamic; Cambridge University Press: New York, 2005. (15) Cheng, H.-P. Water Clusters: Fascinating Hydrogen-Bonding Networks, Solvation Shell Structures, and Proton Motion. J. Phys. Chem. A 1998, 102, 6201−6204. (16) Brudermann, J.; Lohbrandt, P.; Buck, U.; Buch, V. Surface Vibrations of Large Water Clusters by He Atom Scattering. Phys. Rev. Lett. 1998, 80, 2821−2824. (17) Brudermann, J.; Lohbrandt, P.; Buck, U.; Buch, V. Surface Vibrations of Large Water Clusters by Helium Atom Scattering. J. Chem. Phys. 2000, 112, 11038−11047. (18) Zamith, S.; Feiden, P.; Labastie, P.; L’Hermite, J.-M. Erratum: “Attachment Cross Sections of Protonated Water Clusters” [J. Chem. Phys. 133, 154305 (2010)]. J. Chem. Phys. 2014, 141, 139901. (19) Lengyel, J.; Pysanenko, A.; Poterya, V.; Slavíček, P.; Fárník, M.; Kočišek, J.; Fedor, J. Irregular Shapes of Water Clusters Generated in Supersonic Expansions. Phys. Rev. Lett. 2014, 112, 113401. (20) Jönsson, P. G. Hydrogen Bond Studies. CXIII. The Crystal Structure of Ethanol at 87 K. Acta Crystallogr., Sect. B 1976, 32, 232− 235. (21) Tauer, K. J.; Lipscomb, W. N. On the Crystal Structures, Residual Entropy and Dielectric Anomaly of Methanol. Acta Crystallogr. 1952, 5, 606−612. (22) Amad, M. H.; Cech, N. B.; Jackson, G. S.; Enke, C. G. Importance of Gas-Phase Proton Affinities in Determining the Electrospray Ionization Response for Analytes and Solvents. J. Mass Spectrom. 2000, 35, 784−789.

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Attachment of Water and Alcohol Molecules onto Water and Alcohol

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