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Article pubs.acs.org/JPCA Probing Methanol Cluster Growth by Vacuum Ultraviolet Ionization Biswajit Bandyopadhyay, Oleg Kostko, Yigang Fang, and Musahid Ahmed* Chemical Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States S Supporting Information * ABSTRACT: The ability to probe the formation and growth of clusters is key to answering fundamental questions in solvation and nucleation phenomena. Here, we present a mass spectrometric study of methanol cluster dynamics to investigate these two major processes. The clusters are produced in a molecular beam and ionized by vacuum ultraviolet (VUV) radiation at intermediate distances between the nozzle and the skimmer sampling different regimes of the supersonic expansion. The resulting cluster distribution is studied by time-offlight mass spectrometry. Experimental conditions are optimized to produce intermediate size protonated methanol and methanol−water clusters and mass spectra and photoionization onsets and obtained. These results demonstrate that intensity distributions vary significantly at various nozzle to ionization distances. Ion−molecule reactions closer to the nozzle tend to dominate leading to the formation of protonated species. The protonated trimer is found to be the most abundant ion at shorter distances because of a closed solvation shell, a larger photoionization cross section compared to the dimer, and an enhanced neutral tetramer precursor. On the other hand, the protonated dimer becomes the most abundant ion at farther distances because of low neutral density and an enhanced charged protonated monomer−neutral methanol interaction. Thomson’s liquid drop model is used to qualitatively explain the observed distributions. ■ INTRODUCTION Understanding the formation and growth of clusters is an active area of research as these processes in principle can capture the dynamical transition between the isolated gas phase and bulk medium. Cluster growth via ionic association pathways are key processes in aerosol physics1 and low temperature interstellar chemistry.2 The reverse process, i.e., dissociation of larger clusters by photoionization, plays a crucial role in atmospheric chemistry.3,4 Mass spectrometry is a powerful technique to study these processes and we used tunable vacuum ultraviolet (VUV) radiation to study small water clusters5,6 and mixed methanol−water hydrogen-bonded systems7 to decipher photoionization dynamics. Measurements of photoionization onsets and mass spectra provided information on fragmentation mechanisms, ion−molecule reactions, and structural rearrangements of neutral and/or ionized clusters. Continuous supersonic expansions from a small nozzle leads to adiabatic cooling, which results in density and temperature drop.8,9 As the expansion proceeds through the nozzle, numerous collisions between gas atoms produces neutral clusters. If a “seed” is added with the buffer gas, coexpansion produces the clusters of interest. For supersonic expansions, cluster formation and growth have been studied by varying the initial temperature and pressure of the expanding gas.10 Various nozzle shapes and sizes have also been used to study the effects on cluster formation.11 Pulsed laser vaporizations,12 electric discharge techniques,13,14 and electron guns15 routinely produce ionic clusters with different intensity distributions and internal temperatures by sampling the various parts of the © 2015 American Chemical Society supersonic expansion. In those cases, pulsed laser or electron gun timings are adjusted with respect to the gas pulse to sample the regimes of ion−molecule to neutral clustering. For continuous expansions, these regimes in principle can be accessed by varying the photoionization distance from the nozzle. These expansions also provide for a more stable environment compared to pulsed sources by decoupling the fluid dynamics and ionization. In the present work, we report an experimental strategy to systematically study cluster growth and decay processes which are either predominated by ionization induced association and/or dissociation pathways. We produced a continuous molecular beam of methanol and photoionized it at variable distances from the nozzle to sample different regions of the expansion. We chose methanol because of its crucial role in astrochemical processing of hydrocarbons,16−18 atmospheric uptake by ice nanoparticles,19 and local structure of mixed liquids.20 Photoionization properties of alcohol−water clusters are also important in analytical chemistry.21 There have been numerous mass spectrometry based studies of methanol and methanol−water clusters produced by a variety of ionization sources including electron impact, and multi- and single-photon ionization.20,22−38 Photoionization dynamics of these systems are well understood, and hence this experimental approach can Received: January 28, 2015 Revised: April 8, 2015 Published: April 13, 2015 4083 DOI: 10.1021/acs.jpca.5b00912 J. Phys. Chem. A 2015, 119, 4083−4092 Article The Journal of Physical Chemistry A are registered. The photoionization spectrum of xenon has two converging Rydberg series 5p5ns′ and 5p5nd′, the former of which is very narrow. PIE spectra of the 5p58s′ peak are measured using different sizes of the T4 monochromator exit slit and two of the PIE curves are shown in Figure 2a together examine the effect of ionization distance on the mass spectrometry. ■ EXPERIMENTAL SECTION The experiments are carried out in a continuous supersonic expansion cluster machine coupled to a three meter VUV monochromator of a newly commissioned terminal (T4) on the Chemical Dynamics Beamline (9.0.2), located at the Advanced Light Source, Berkeley, California. Figure 1 shows a Figure 1. Cross-sectional view of the molecular beam machine. schematic of the experiment. One bar of argon is passed through a bubbler containing 99.9% pure methanol and expanded through a 100 μm nozzle to a differentially pumped chamber which is kept at a pressure of 2 × 10−4 Torr during the expansion. The molecular beam is intersected with the VUV radiation at various axial distances from the nozzle (x = 2−25 mm) and the resulting cluster ions are sampled into a time-offlight mass spectrometer. The ionization distance is varied by changing the nozzle position with respect to the point of intersection of molecular and VUV beams. The VUV beam is rectangular with a dimension of 1000 × 330 μm2. A set of four electrodes are used to guide the ions from the ionization region to the mass spectrometer through a skimmer. The lenses are kept at small potentials (+5, 0, −3, and 0 V, respectively) and the skimmer is grounded. The mass spectrometer is kept at 2 × 10−6 Torr in a second differentially pumped chamber. A start pulse for the TOF is provided by pulsing the repeller and accelerator plates because of the quasi-continuous (500 MHz) nature of the synchrotron light. The ions are pulse-extracted by fast switching of repeller and accelerator plates to 1100 V using a pulse width of 7.0 μs. Ions are accelerated perpendicularly to their initial flight path through the field free region and detected by a microchannel plate (MCP) detector which is installed at the end of the flight tube. Mass spectrometer settings are kept fixed while ionization distances are varied. The time dependent electrical signal from the detector is amplified by a fast preamplifier, collected by a multichannel scalar card, and then integrated with a computer. TOF spectra are measured at different positions in the photon energy range between 9.5 and 13.0 eV. The photoionization efficiency (PIE) curves are obtained by integrating peak intensities at each photon energy and normalized by the photon flux. The molecular beam end-station is used to measure the resolution of terminal T4’s three meter normal incidence monochromator (McPherson, Inc., Chelmsford, MA). PIE measurements are performed on a mixture of 2% xenon in helium and intensities of Xe peaks in time-of-flight mass spectra Figure 2. (a) Xenon 5p58s′ resonance shown after subtraction of underlying broad 5p56d′ peak for two sizes of T4 monochromator exit slit: 100 and 600 μm. Red lines represent a Gaussian function fit to experimental data, the dependence of the full width at half-maximum (fwhm) on width of T4 monochromator exit slit is shown in panel (b). Error bars in panel (b) correspond to standard deviation of 2σ. with a Gaussian fit. The dependence of full width at halfmaximum (fwhm) of the Gaussian on the exit slit size is shown in Figure 2b. Most of the experimental data points have a linear dependence. Only for the slit size below 100 μm do the experimental points start to deviate from linear dependence, converging to a maximum resolving power (E/ΔE) of 1000. The T4 photon flux is measured by a silicon photodiode SXUV-100 (Opto Diode Corp.) whose quantum efficiency is known. The flux under typical operational conditions is about 2 × 1013 photons/s. ■ RESULTS A. Mass Spectrometry of Methanol Clusters. Figure 3 displays a representative mass spectrum measured at a distance of 10 mm from the nozzle at 11 eV photon energy. The main ions observed in this experiment are similar to those in which VUV ionization was performed inside the mass-spectrometer chamber (MS-ionization).7 Protonated methanol clusters [H+(CH3OH)n] show the most intense distribution followed b y a m u ch w e ak e r p r o t o n a t e d m e t h a n o l− wa te r [H+(CH3OH)nH2O]. Unprotonated species apart from methanol monomer are not observed. Intermediate sizes (n ∼ 30) are observed for both protonated methanol and methanol− water clusters. Protonated methanol dimethyl ether progression 4084 DOI: 10.1021/acs.jpca.5b00912 J. Phys. Chem. A 2015, 119, 4083−4092 Article The Journal of Physical Chemistry A Figure 3. Mass spectrum showing various cluster distributions measured at an ionization distance of 10 mm from the nozzle at 11 eV photon energy. Expanded view of protonated methanol and methanol dimethyl ether distributions are shown in insets. Figure 4. Intensity distributions of protonated methanol and methanol−water clusters measured at x = 2, 15, 20, and 25 mm. Ion intensities are plotted in logarithmic scale to highlight the prominent distributions observed for these two species. Inset in the upper trace shows the expanded view for n = 1−5. [H+(CH3OH)n(CH3)2O] is also detected, albeit the signal is relatively small compared to the other cluster distributions. The appearance of protonated methanol upon ionization has been observed previously using electron impact and single and multiphoton ionizations.7,23,25,26,32,35,37−39 The mechanisms of methanol and methanol−water22,34 cluster formation were discussed in these earlier studies and here we will briefly describe some of the key features. It has been suggested that the ionization of neutral hydrogen bonded clusters leads to the formation of protonated cluster ions via rapid proton transfer and fragmentation: distances, while the dimer is the most abundant ion at x = 20 mm. For n = 4−30, the overall ion intensities decrease with increasing ionization distances. There are some interesting features observed for these distances. At x = 2 mm, a gradual slow decrease is observed for n = 4−30. Mass spectra at all other distances show a general trend in the n = 4−30 range: a rapid decay at smaller clusters followed by a slow rise to intermediate sizes, and a moderate fall at larger species. As the distance increases, the intensities of smaller clusters decay more rapidly and an inverted-well shaped distribution is observed for the intermediate sizes. The maximum of this well increases with distance. For H+(CH3OH)nH2O, clusters up to n = 4 are not detected and n = 5−6 are very weak; a plateau is observed from n = 8−30 with a maximum around n = 15. As the ionization distance increases, the intensity of a specific size decreases, similar to those observed for protonated methanol clusters. C. Photoionization Efficiency (PIE) Curves and Appearance Energies (AE) at Various Distances. Figures 5 and 6 display the PIE curves of methanol and protonated methanol clusters measured in the 9.5−13.0 eV region. Figure 5 depicts PIE curves for each species with distance variation while Figure 6 shows PIE curves for different species while keeping the distance fixed to highlight trends in the mass spectra. The appearance energies (AE) for monomer cation and protonated clusters evaluated from the PIE curves are tabulated in Table S1 in the Supporting Information file (SI). The AE of methanol was found to be the same (10.8 eV) for MSand in-source ionization. AE values obtained for protonated methanol monomer, dimer, and trimer are in the range of 10.1−10.3, 9.8−10.1, and 9.6−10.1, respectively. Previous work from our group has shown that the ionization energy of methanol decreases upon clustering, reaching an asymptotic limit of around 9.8 eV for a cluster of size ≥4.7 PIE curves of the unprotonated monomer cation at various distances show sharp rise at 10.8 eV and this value is exactly the same as obtained for MS ionization. PIE curves of the protonated monomer shows a (CH3OH)n + hν → (CH3OH)+n + e− → H+(CH3OH)n − 1 + CH3O + e− (1) Protonated methanol−water are formed either from neutral methanol−water cluster (CH3OH)n H 2O + hν → H+(CH3OH)n − 1H 2O + CH3O + e− (2) or from protonated methanol clusters H+(CH3OH)n → H+(CH3OH)n − 2 H 2O + (CH3)2 O (3) Castleman and Garvey have suggested that reaction 3 occurs for size n ≥ 9 since the lowest cluster size observed was H+(CH3OH)7.23−25,34 Morgan and Castleman23 have also suggested that this reaction does not occur for the smaller clusters, since the formation of a methyl bound complex intermediate is not facile. In our experimental conditions, n = 8 and 9 are more intense than n = 7 in the mixed methanol− water cluster series indicating that the observed distribution arises from reaction 4. B. Intensity Distribution of Cluster Ions at Various Distances. Figure 4 depicts the integrated intensities of protonated methanol [H+(CH3OH)n] and methanol−water [H+(CH3OH)nH2O] clusters at four various ionization distances (x = 2, 15, 20, 25 mm). Intensities are shown in logarithmic scale to highlight the interesting size distributions. For H+(CH3OH)n, relative intensities of smaller sizes (n = 1− 3) do not change significantly at all distances. The protonated methanol trimer is found to be the most intense ion at shorter 4085 DOI: 10.1021/acs.jpca.5b00912 J. Phys. Chem. A 2015, 119, 4083−4092 Article The Journal of Physical Chemistry A Figure 5. PIE curves for methanol (M+) and protonated methanol clusters (MnH+) at various distances. Insets show the expanded view showing the onsets of ionization. Figure 6. PIE curves for methanol (M+) and protonated methanol clusters (MnH+) at x = 2, 15, 20 and 25 mm. small shoulder around 10.2 eV and sharp rise at 10.8 eV. As distance increases, AE values change slightly (on the order of ∼100−150 meV) for monomer. The change in AE values is most prominent for trimer, where the difference in AE between x = 2 and 25 mm is about 500 meV. PIE curves for these species also show some interesting features as the distance and photon energies are varied. For all distances, the methanol cation shows a sharp rise at 10.8 eV and then a gradual decrease up to 13 eV (Figure 5). Here, it should be noted that all the PIE curves have an absorption due to argon (used in the gas filter of the beamline to remove higher harmonics) at 11.8 eV. For protonated methanol at 2 mm, after a sharp rise at 10.8 eV, a rapid decay (around 11 eV) followed by a sharp rise (at around 12.5 eV) is observed. At farther distances, a gradual increase in ionization efficiency is seen (ignoring the dip at around 11.8 eV). For dimer and trimer at 2 mm, PIE curves show a slow rise from 9.5 to 12.5, followed by a sharp increase. For the farthest distances, the curves show a slow rise up to 10.8 eV and then a rapid increase due to methanol absorption. The PIE curve for the methanol cation crosses that of the protonated methanol around 12.25 eV at all distances (Figure 6). At x = 2 mm, the dimer and trimer show a slow rise at lower 4086 DOI: 10.1021/acs.jpca.5b00912 J. Phys. Chem. A 2015, 119, 4083−4092 Article The Journal of Physical Chemistry A Figure 7. (a) Schematic of a supersonic expansion. (b) A COMSOL simulation of a nozzle of diameter 100 μm. Distances are in mm. clusters to get an idea if a liquid-like property is indicated by the intensity distributions. A general theory of cluster growth processes (Thomson’s liquid drop model) will be discussed for data analysis to explain the observed distributions at various distances. A. Characterization of the Supersonic Expansion. Supersonic expansion from a small nozzle leads to adiabatic cooling, resulting in rapid temperature and density drop as the expansion proceeds farther from the nozzle. Clusters are formed as a result of sufficient collisions close to the exit before the expansion becomes rarefied and cooling stops. Figure 7a shows a schematic of a supersonic jet expansion into a region of background pressure Pb. The gas accelerates in the nozzle throat where Mach number (M) becomes close to 1 at the exit and continues to accelerate (M ≫ 1) up to the Mach disc. energies and crosses the monomer curve twice: once at 11.1 eV and again around 12.3−12.4 eV. For all other distances after the initial rise, dimer and trimer show steady ionization yields in the 11.0−13.0 eV range. ■ DISCUSSION Mass spectrometry and photoionization dynamics of methanol clusters have been well studied, and here we will mostly discuss the effect of variable ionization distance. In doing so, we will first briefly describe the supersonic expansion from a small nozzle and how cluster generation can be influenced by changing the distance. In the following section, the intensity distributions, PIE curves, and AEs for small clusters will be discussed to explain the effect of distance on these features. Finally, we will discuss the transition from small to intermediate 4087 DOI: 10.1021/acs.jpca.5b00912 J. Phys. Chem. A 2015, 119, 4083−4092 Article The Journal of Physical Chemistry A and at 25 mm, the dimer is clearly the most abundant ion. The other interesting feature is the relative populations of the intermediate sized clusters. At 2 mm, after the initial rise from n = 1−3, the relative population decreases gradually showing an almost smooth distribution. On the other hand, as the distance increases, intermediate size clusters go through a maximum. In our previous study (MS-ionization), we found that the protonated methanol trimer is the most stable ion up to 14 eV photon energy. This observation is consistent with several other studies, including an electron impact26,32 one, where a closed solvation shell is proposed around a protonated methanol ion. In our case, the protonated trimer is the most abundant ion at 2 mm probably because of three factors: (a) closed solvation shell around a protonated methanol; (b) photoionization cross section is greater than the dimer up to 14 eV energy; and (c) enhancement of the neutral tetramer precursor at closer distances since the neutral density is higher. The protonated dimer becomes the most stable ion above 14 eV energy (in MS ionization) and also at farther ionization distances (in-source ionization). The dimer is most stable ion beyond 14 eV, as discussed in our previous work, because clusters with higher internal energies tend to fragment to lower sizes via evaporative cooling. In the in-source ionization scheme, the neutral density decreases as the expansion is moved farther from the nozzle. Up to the point of ionization, neutral clusters which are produced during the supersonic expansion remain unperturbed. As the distance increases, neutral density decreases and condensation around a charged species would be more probable for monomer (making a protonated dimer cation) rather than a dimer which would make a protonated trimer ion. Ion−molecule reactions involving the protonated monomer cation is unlikely since unprotonated clusters other than monomer cation are not observed. The AE of methanol monomer is found to be 10.8 eV at all distances (Figures 5 and 6). The AEs of protonated clusters are shifted around 100−300 meV as a function of distance. The AE of protonated monomer is in the range of 10.1−10.3 eV, similar to that found in the MSionization study. Since at all distances, the AEs do not shift closer to or are greater than the IE of methanol, it is clear that the protonated monomer is formed from fragmentation of larger clusters. This situation is also true for the protonated dimer and trimer, where for all distances, the AE of the protonated dimer is less than that of the protonated monomer; similarly, the AE of the trimer is less than that of the dimer. Another interesting feature is that at higher energies, the ionization yield of the monomer cation goes down at all distances, whereas in the case of the dimer and trimer, the yield is steady at all energies except at 2 mm ionization distance. At 2 mm, for dimer and trimer, the initial rise in the PIE curve is slow and gradual but shows a sharp rise at higher energies indicating that evaporative cooling from the higher cluster leads to more dimers and trimers. The evaporative cooling effect is not observed when the ionization is carried out at farther distances. Having described the nature of mass spectrometry and PIE curves of small clusters, we now discuss the effect of ion− molecule reactions to the cluster distributions. The thermochemistry of methanol and methanol−water clustering has been studied by Kebarle and Meot-Ner.26−28 They have computed enthalpy (ΔH), entropy (ΔS), and free energies (ΔG) of formation of reaction 4 Mach disc location (xM) is related to the nozzle diameter (d), stagnation pressure (P0), and background pressure (Pb) in a very simple but accurate empirical form P xM = 0.67 b d P0 We use the nozzle diameter (100 μm) and pressure values from our experiment to the above expression and obtain a Mach disc position of ∼67 mm. The “zone of silence” is the core of the jet bounded by the barrel shock and the Mach disc. This is a region of very low pressure and molecular beams are extracted from it. Figure 7b shows a representation of the expansion from a 100 μm nozzle by solving the Navier−Stokes (N−S) equations using the COMSOL multiphysics software package. We assumed that the gas flow in the interfacial region remains at near thermal equilibrium continuum. This treatment is similar to continuum models applied in previous studies which used different nozzles and mass spectrometers.40,41 The complete description and parameters used for solving this model are provided in the SI. We have used the high Mach number flow module in the COMSOL multiphysics, which is valid for Knudsen number <0.1. The Knudsen number (λ/d) in the high Mach number and low pressure region becomes high as flow expands downstream from the nozzle. Therefore, a continuum model is not strictly valid for our case. However, it has been reported that even though noncontinuum effects in high-speed expanding flow would change the thermal structure of the gas, dynamic features such as velocity and temperature are not strongly perturbed.42,43 Here, we present our nozzle picture to show that velocity and temperature reach their optimum values within 10−20 nozzle diameter (1−2 mm for 100 μm nozzle). The description is also consistent with the Method of Characteristics calculations by Miller.8 The picture in Figure 7b depicts an upward flow stream with nozzle situated at 9 mm. The maximum velocity is reached at the exit of the nozzle (800 m/s) and then falls down to subsonic speed (200 m/s). The temperature also changes rapidly from 300 to 150 K within 1 mm distance from the nozzle diameter. Therefore, a continuum model is not sufficient for a complete description of the expansion. B. Cluster Generation Mechanisms, Mass Spectra, and PIEs as Functions of Ionization Distance. Since the collisions are maximum right at the nozzle exit and cooling stops within 10−20 nozzle diameter, maximum neutral clustering occurs at that region. As the expansion proceeds, the continuum flow quickly becomes a molecular flow where the neutral density is quite low. A VUV photon whose energy is greater than the ionization energy of methanol can ionize methanol monomer producing a methanol cation. Cluster ionization energies are generally less than that of the monomer, and therefore neutral clusters are ionized at an energy lower than the ionization energy of the monomer. Within the ionized clusters, proton transfer can produce a protonated methanol ion, and clusters then tend to rearrange around this newly formed charged species. Similar observations can be found for water clusters, where upon ionization protonated water clusters form around a core H3O+.5 The relative intensities of protonated methanol clusters, H+(CH3OH)n, change significantly with distance. As shown in Figure 4, for distances up to 15 mm, the protonated trimer is the most intense ion in mass spectra. At 20 mm, the relative intensities between dimer and trimer are almost comparable, 4088 DOI: 10.1021/acs.jpca.5b00912 J. Phys. Chem. A 2015, 119, 4083−4092 Article The Journal of Physical Chemistry A Figure 8. Free energy of formation (ΔG) as a function of number of molecules (n) and different supersaturation ratios (S) according to Thomson’s model. While (a) shows a short-range of change in S, (b) shows the change from S = 1.6 to 10. H+(CH3OH)n − 1 + CH3OH → H+(CH3OH)n its mathematical form is correct which can provide a qualitative picture of the process.48 Thomson’s model is based on the thermodynamics of a liquid drop at equilibrium, which uses bulk variables such as surface tension and dielectric constants. Therefore, application of this model to molecular beam studies has been criticized and Castleman et al. have shown that it does not agree with experimental thermodynamic values for many small clusters. This model agrees better with the experiment when the cluster sizes are fairly large.51 Fenn et al. argued that supersonic jets are not equilibrium systems and clustering environment changes very rapidly as the expansion proceeds farther away from the source. For the clustering of protonated water in a supersonic jet, they have expressed nucleation in terms of the rate constants of individual association reactions leading to the formation of the ion cluster prenucleation embryos.53 Castleman et al. have shown that thermodynamic steady state and kinetic model can be complementary at certain conditions.48 A simple mathematical formulation of equivalence between these two models based on Castleman’s study is given in SI. According to Thomson’s equation, the free energy change (ΔG) associated with formation of the nth cluster is given by (4) For reaction 4, the computed ΔH values are on the order of 31.6−33.1 kcal/mol for monomer to dimer formation. These values gradually decrease as protonated methanol is solvated by methanol molecules. The ΔH values changes from 21.0 to 14.0 kcal/mol for n = 2 → 3 to n = 3 → 4 clustering. Meot-Ner and co-workers have suggested that the change in ΔH is due to the closure of the first solvation shell. They have also found that the limiting value for the higher cluster formation is 9.0 kcal/mol, which is equivalent to the condensation enthalpy of methanol. They have suggested that if the clustering reactions involved only the formation of single new hydrogen bond, this limiting value would be 5 kcal/mol. Therefore, the observed value indicates that higher clusters possess similar intermolecular forces as that exists in the bulk liquid. This would suggest that hydrogen-bonding, dipole−dipole, dipole−induced dipole, and hydrophobic interactions among the alkyl group play crucial roles in larger clusters similar to liquid methanol. As a result, larger clusters may not have a purely hydrogen bonded chain, but a liquid-like structure. Recent infrared spectroscopy study of (CH3OH)n and H+(CH3OH)n suggested that the spectrum of protonated methanol 50 (n = 50) converges to that of liquid methanol.44 The observed O−H frequency of liquid methanol is slightly higher than that of the n = 50. This difference suggests that the major hydrogen bonding network in liquid is much shorter than n ∼ 10. Molecular dynamics simulations also predict this perception.45,46 Discussion of our next section is prompted by these findings. C. Thomson’s Liquid Drop Model and Its Relation to Intensity Distributions. Adiabatic cooling during supersonic expansions leads to a high degree of supersaturation, and clusters can nucleate to form droplets. Supersonic expansions in fact have been realized as fast flow reactors and proposed as tools to study nucleation.47,48 However, nucleation rates are strongly dependent on the temperature, and since the clustering environment changes so rapidly during the expansion, it is difficult to obtain a reliable kinetic model. Developing a complete model of cluster distribution under our experimental photoionization condition is beyond the scope of this study. However, we would like to propose a simplified version based on Thomson’s liquid drop model.49−51 This model has been used to discuss ion-induced nucleation in molecular beams and cloud chamber experiments. Even though Thomson’s equation is inaccurate for quantitative estimates,52 ΔGn = −nkBT ln(S) + 4πrn2σ + q2 ⎛ 1 ⎞⎟⎛ 1 1⎞ ⎜1 − ⎜ − ⎟ 8πε0 ⎝ ε ⎠⎝ rn ri ⎠ (5) where n, kB, T, and S are the number of molecules, Boltzmann constant, temperature, and supersaturation ratio, respectively. The first term of Thomson’s equation is the volume excess free energy, i.e., energy gain due to the vapor → liquid phase transition. The second term represents the surface excess energy, i.e., energy required to form a neutral drop of radius rn. The third term is the free energy change induced by an ion of radius ri and charge q. ε0 and ε are the vacuum permittivity and dielectric constant, respectively. This term represents the energy required to solvate the charged droplet which contributes to the lowering of the cluster free energy due to the presence of an ion. Figure 8 displays the free energy of formation as a function of number of molecules for methanol clusters around a protonated methanol ion at different temperatures and supersaturation values according to Thomson’s model. Here we reiterate that this model is qualitative and there is no way to find temperature or supersaturation values from our experi4089 DOI: 10.1021/acs.jpca.5b00912 J. Phys. Chem. A 2015, 119, 4083−4092 Article The Journal of Physical Chemistry A clusters and lowering of AEs suggest that ion−molecule reactions involving methanol monomer cation do not occur. PIE curves at short distances show that at higher energies, evaporative cooling produces more protonated methanol monomer, dimer, and trimer. The evaporative cooling effect is not observed for farther distances. The intensity distributions at various distances are qualitatively explained by Thomson’s liquid drop model. At closer distances, both supersaturation and ion-induced growth reduces the free energy barrier of formation. On the other hand, low neutral density at farther distances increase the free energy barrier, reducing the ioninduced growth. This experimental approach with a control on growth and decay processes can be further implemented to new directions. One example would be to study ion−molecule association reactions.54 Dissociation of organic cluster molecules via ionization can be simultaneously studied using the same approach. An experiment would be to study the photoionization dynamics of mixed systems in which constituents have different ionization energies, and one can tune VUV light into different ionization regimes to see how chemistry changes during a reaction. Toward this end, ion−molecule reactions of mixed clusters of acetylene (IE = 11.5 eV) and ethylene (IE = 10.5 eV) are being investigated focusing on photoionization dynamics. ment. However, we can assume that during the expansion, these two values are interdependent and change rapidly along the centerline. We use a temperature of 30 K computed using the Method of Characteristics,8 which corresponds to a value very close to the nozzle throat. At the lowest supersaturation value (S = 1.6), the free energy shows a rapid decay at smaller n, followed by an inverted well with a maximum. According to Thomson’s model, this is referred to as the barrier of nucleation. As S increases, the maximum in free energy decreases indicating a reduced barrier. At higher supersaturation values, free energy decreases with no barrier. At these S values, the process is essentially controlled by the kinetics of cluster formation. Here, it should also be noted that varying the temperature in eq 5 does not change the shape of the curve, only the free energy values changes linearly if S is fixed. The model curves show a rapid decrease in ΔG for smaller sizes with a minimum in free energy corresponding to n ≈ 20−25 sizes, and mass spectra at all ionization distances show an increasing trend in intensity with a maximum at n = 3. After the initial rapid rise in intensity, distributions for n = 4− 30 show a decay followed by a maximum, which can be described by the model, where free energy shows a small rise followed by the barrier. The intensity distribution at different ionization distances provides two salient features: (a) supersaturation decreases as the expansion proceeds downstream; (b) as ionization occurs closer to the nozzle, protonated cations induce ion−molecule reactions. On the other hand, neutral clusters can remain unperturbed up to the ionization distance. Now, we see that the distribution corresponding to the shorter ionization distance (2 mm) is qualitatively similar to that of the model curve with higher S (1.9, 4, or 10) values where the free energy barrier virtually does not exist. This makes sense because we expect a higher supersaturation at shorter distances, and a lower energy barrier due to the ion-induced lowering of free energy. The neutral density decreases with distance and therefore the barrier increases. The supersaturation also decreases as ionization is carried out farther from the nozzle, resulting in an increased energy barrier. ■ ASSOCIATED CONTENT S Supporting Information * Brief description of Navier−Stokes equations; boundary conditions to solve these equations for supersonic expansion from a small nozzle; parameters and values used to calculate free energies using Thomson’s equation; and equivalence between the kinetic and thermodynamic steady state models. This material is available free of charge via the Internet at http://pubs.acs.org. ■ ■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. CONCLUSIONS We have studied intensity distributions of methanol clusters by VUV photoionization mass spectrometry where ionization is carried out at variable distances from the nozzle. The photoionization of methanol produces clusters of protonated methanol, methanol−water, and methanol dimethyl ether. Photoionization of a neutral hydrogen bonded methanol cluster undergo a rapid proton transfer reaction. The cluster then condense around the newly formed protonated methanol via a series of ion−molecule reactions. The intensity distributions at various ionization distances change significantly for both smaller complexes and intermediate clusters. For shorter distances, the protonated trimer is found to be the most abundant ion similar to the MS ionization study. This ion is the most abundant at shorter distances because of a closed solvation shell, a larger photoionization cross section than that of the dimer, and an enhanced neutral tetramer precursor. The protonated dimer becomes the most abundant ion at farther distances because of low neutral density and an enhanced charged protonated monomer−neutral methanol interaction. PIE curves are measured for small complexes from 9.5 to 13.0 eV at each distance which shows that appearance energies are shifted to lower values due to protonation and clustering. The absence of unprotonated Notes The authors declare no competing financial interest. ■ ACKNOWLEDGMENTS This work and the Advanced Light Source are supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC0205CH11231. ■ REFERENCES (1) Enghoff, M. B.; Svensmark, H. The Role of Atmospheric Ions in Aerosol Nucleation - a Review. Atmos. Chem. Phys. 2008, 8, 4911− 4923. (2) Herbst, E. The Chemistry of Interstellar Space. Chem. Soc. Rev. 2001, 30, 168−176. (3) Seinfeld, J. H. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; J. Wiley, 2006. (4) Vehkamaki, H.; Riipinen, I. Thermodynamics and Kinetics of Atmospheric Aerosol Particle Formation and Growth. Chem. Soc. Rev. 2012, 41, 5160−5160. 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