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Change (IPCC), 1995; U.S. Environmental Protection .... a total N2 flow rate of $15 STP L minА1) were mixed in a ... $0.8 atm (610 torr.) ... water partial pressures lower than this, H2SO4 coming off ... would be 200 parts per trillion by volume (pptv; one pptv ..... molА1 can be used as an upper limit for ∆G for the reaction.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D12, 4158, 10.1029/2001JD001100, 2002

Measurement of prenucleation molecular clusters in the NH3, H2SO4, H2O system D. R. Hanson and F. L. Eisele1 Atmospheric Chemistry Division, National Center for Atmospheric Research, Boulder, Colorado, USA Received 16 July 2001; revised 30 November 2001; accepted 3 December 2001; published 29 June 2002.

[1] The molecular cluster ions HSO4(H2SO4)n1(NH3)m corresponding to the neutral

species (H2SO4)n(NH3)m for n = 2 to 6 and m = 0 to n1 have been observed at temperatures up to 285 K. A transverse chemical ionization apparatus was located inside a cooled flow tube where water, sulfuric acid, and ammonia vapors mixed and formed clusters. The complexities of the experimental technique and the interpretation of the results are extensively discussed. Typical NH3 and H2SO4 concentrations were 2  109 cm3, i.e, 100 pptv at atmospheric pressure. For these conditions, cluster concentrations were estimated to be a few times 106 cm3 and the critical, particle-forming cluster likely contained 2 H2SO4 molecules at 275 K. The results are consistent with the species (H2SO4)2NH3 playing an important role in the formation of new particles in the atmosphere. INDEX TERMS: 0305 Atmospheric Composition and Structure: Aerosols and particles (0345, 4801); 0317 Atmospheric Composition and Structure: Chemical kinetic and photochemical properties; 0335 Atmospheric Composition and Structure: Ion chemistry of the atmosphere (2419, 2427); 0394 Atmospheric Composition and Structure: Instruments and techniques; KEYWORDS: ammonia, sulfuric acid, nucleation, molecular clusters, particle formation

1. Introduction [2] Atmospheric aerosol particles can have a large influence on radiative forcing of climate and are also believed to pose a health hazard [Intergovernmental Panel on Climate Change (IPCC), 1995; U.S. Environmental Protection Agency, 1997]. For these and other reasons, research on the sources of these particles is very important. Gas-toparticle nucleation involving H2SO4 vapor has long been believed to be a robust source of atmospheric particles. A number of recent studies have shown a strong correlation between H2SO4 and new particles [Weber et al., 1999; Birmili et al., 2000]; however, the process by which these particles are formed is not well understood. Recently, ammonia vapor has been proposed as a potential key player in the formation of atmospheric particles [Coffman and Hegg, 1995; Larsen et al., 1997; Ball et al., 1999; Korhonen et al., 1999]. [3] In a recent paper [Eisele and Hanson, 2000] we described an apparatus designed to measure molecular clusters of sulfuric acid under quiescent (as opposed to free jet expansion) particle-growth conditions. Neutral H2SO4 clusters containing 2 to 8 H2SO4 molecules at 240 K were detected. The cluster measurements were performed for H2SO4 concentrations of 1 – 2  109 cm3, much greater than would be found in the atmosphere and were conducted at temperatures of 240 K and relative humidities (RH) of 15 to

1 Also at School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA.

Copyright 2002 by the American Geophysical Union. 0148-0227/02/2001JD001100

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60%. The critical cluster was found to contain 3 to 4 H2SO4 molecules and its abundance was as high as 107 cm3. [4] This technique provides a window through which particle nucleation can be observed, and in this paper we extend the system to include ammonia vapor. For example, molecular clustering involving H2SO4 and NH3 can be illustrated as H2 SO4 þ H2 SO4 þ NH3 $ ðH2 SO4 Þ2 þ NH3 $ ðH2 SO4 Þ2 NH3 ð1aÞ H2 SO4 þ ðH2 SO4 Þ2 NH3 þ ðm0  1ÞNH3 $ ðH2 SO4 Þ3 ðNH3 Þm ; ð1bÞ ... H2 SO4 þðH2 SO4 Þn1 ðNH3 Þ * þðmm*ÞNH3 $ðH2 SO4 ÞnðNH3 Þm : m ð1cÞ

For the sake of simplicity, H2O molecules are not taken into account here. Note that (H2SO4)n(NH3)m can be written in shorthand as (n, m). The monomer reactants H2SO4 and NH3 are indicated as separate entities, but they may be associated (i.e., as NH3.H2SO4) or they may add stepwise to a cluster. Note that reactions (1a) – (1c) are only to illustrate the clustering processes and some equations are composed of multiple steps. [5] Here we report the observation of (H2SO4)n(NH3)m clusters for n = 2 to 6 and m < n at number densities up to several 106 cm3. We detected these clusters at temperatures up to 285 K; much warmer than those necessary to form detectable levels of clusters in the H2SO4-H2O system

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(240 K [Eisele and Hanson, 2000]). A number of tests designed to understand the ionization and detection of these clusters are presented, and several potential problems are identified and thoroughly discussed. Also, a computational fluid dynamics model [Fluent Incorporated, 1999] was employed to gain a better understanding of the flow, temperature profile, and reactant concentrations within the flow reactor. We present evidence that the critical cluster, the cluster accountable for the formation of stable particles, contains three or fewer H2SO4 molecules and two or fewer NH3 molecules.

2. Experimental Method [6] The measurement of H2SO4 and NH3 vapors and their molecular clusters were made in a thermostatted flow tube using chemical ionization mass spectrometry (CIMS). The apparatus is described in detail by Eisele and Hanson [2000], and here a brief description is given along with details of significant changes in the experiment. As previously discussed in that paper, H2SO4 and the clusters (H2SO4)n(H2O)m were monitored by reacting them with NO 3 (HNO3)1,2 ions [Viggiano et al., 1997]. Here, the reaction proceeds as ðH2 SO4 Þn ðNH3 Þm þ NO 3 ðHNO3 Þ1;2 ! HSO 4 ðH2 SO4 Þn1 ðNH3 Þm þ 2; 3ðHNO3 Þ:

ð2Þ

This equation is written assuming the HNO3 ligands do not associate with the HSO4 core ions and that these core ions do not lose H2SO4 or NH3 ligands upon ionization. The assumptions about HNO3 and NH3 are made for conciseness, and their validity does not in general significantly affect our interpretation of the experimental results. Note that H2O molecules are not included in reaction (2). As demonstrated by Eisele and Hanson [2000], neutral sulfuric acid clusters that contain H2O molecules easily lose them upon ionization and/or sampling, but the H2SO4 content of a cluster is preserved due to the high affinity that H2SO4 molecules have for HSO4. Thus, despite the loss of H2O and, to a lesser extent, NH3 molecules upon ionization and sampling, much can be learned about prenucleation clusters in the H2SO4/NH3 system. It is convenient to introduce a shorthand nomenclature (1&n, m) for the ionic species HSO4(H2SO4)n(NH3)m, which indicates one bisulfate ion + nH2SO4 and mNH3 molecules. [7] A flow of N2 carrier gas was directed over liquid sulfuric acid (98 wt%) and another was humidified to provide separate control of the [H2SO4] and of relative humidity. These flows and an additional flow of N2 (to make a total N2 flow rate of 15 STP L min1) were mixed in a region held at 300 K. The gas passed through an aluminum heat exchanger and into the vertically aligned flow tube (9.5 cm ID  110 cm in length) the majority of which is surrounded by a jacket through which a thermostatted coolant was circulated. The average flow speed down the tube was 4 cm s1. Located 40 cm into the cooled region (and 50 cm below the heat exchanger) were ports for the CIMS ion source and mass spectrometer inlet. These extended into the flow tube and were 3.5 cm apart to provide in situ detection transverse to the gas flow [see Eisele and Hanson, 2000, Figure 1]. The voltage difference between the source

and inlet determined the ion-molecule reaction time. A variable ion-molecule reaction time provided a means to distinguish between ionization of neutral H2SO4 clusters and ion-molecule clusters produced by stepwise addition of H2SO4 or NH3 molecules to HSO4 ions [Eisele and Hanson, 2000]. H2SO4 and NH3 concentrations ranged from 0.7– 3  109 and 1– 10  109 cm3, respectively. Total pressure was 0.8 atm (610 torr.) The flow tube temperature Tf was held at 260 to 283 K to induce formation of neutral clusters of H2SO4 and NH3 (a comparison experiment in the H2SO4 – H2O system was performed at 243 K). [8] Water vapor was present typically at a partial pressure of 0.23 torr, although a few mass spectrums were taken at pH2O up to 3 torr. The pH2O of 0.23 torr is equivalent to a relative humidity of 10% at 265 K and 5% at 275 K. For water partial pressures lower than this, H2SO4 coming off the mixing region walls became noticable. For higher water contents the mass spectrum became quite complicated, littered with NO 3 (HNO3)1,2(H2O)x and other ions. Note the pressure in the collisional dissociation chamber (CDC) was 0.01 torr. The CDC is schematically presented in Figure 1b and in Figure 1 of Eisele and Hanson [2000]. In that study of the H2SO4 – H2O system the pressure in the CDC was 0.08 torr. A lower pressure here was chosen to minimize stripping of NH3 from cluster ions. However, that lower pressure also causes the stripping of water molecules from cluster ions to be less efficient. Therefore the water content in the flow reactor was kept relatively low to minimize interferences with the cluster ion signals. As a test of this setup, the flow tube was cooled to 243 K to reinvestigate the clusters formed in the H2SO4 –H2O system. [9] As in our previous study, the temperature of the gas in the flow tube was not uniform owing to the cooling that the gas must undergo. The gas temperature at the level of the mass spectrometer inlet was found to be [Eisele and Hanson, 2000] 2 – 4 K warmer than the wall (depending on proximity to the flow tube wall). This measurement was repeated here, and a comparable temperature difference was observed. Also, the fluid dynamics model (details given below) showed the gas temperature was 1 K warmer than the flow tube wall in this region. We report the temperature of the gas in the detection region to be 2 K warmer than the flow tube wall (uncertainty of ±1 K). 2.1. NH3 [10] Ammonia vapor entered the flow tube through a separate inlet located 25 cm above the detection region. Low levels of [NH3] were accomplished by passing a dilute NH3 (27 ppmv) in N2 mixture through a dilution system [Ball et al., 1999] resulting in a 30 sccm (STP cm3 min1) flow of N2 containing 10 to 100 ppbv NH3. This flow entered the main flow through the inlet, a 1/8 inch (0.32 cm) OD Teflon tube, whose end was a distance of 25 cm upstream of the detection region. The inlet was positioned slightly off the center of the tube based on maximizing the cluster signals. The cluster signals were not extremely sensitive to this position; e.g., they varied 10 to 30% when the injector was moved 1 cm either way off the maximum setting. Assuming NH3 is not lost on surfaces and it is fully mixed in the main flow, the average NH3 concentration would be 200 parts per trillion by volume (pptv; one pptv here is equal to 2.2  107 molecules cm3) from an initial

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Figure 1. Results from computational fluid dynamics (CFD) simulation of the flow reactor with addition of NH3. (a) Lower half of the reactor in cross section is shown with the axial distance from the beginning of the cooled portion of the reactor indicated along one side. The ammonia inlet is the small tube 25 cm into the flow reactor; the ionization region is located at 50 cm. [ NH3] indicated in mixing ratio contours at 5 pptv intervals. (b) Radial cross section at 50 cm. The ion source and the mass spectrometer inlet are overlaid on this plot. 100 ppbv ammonia in the NH3 inlet flow. In the flow reactor, however, there is efficient loss due to H2SO4 on surfaces. Also, the time allowed for NH3 to diffuse into the main flow may not be sufficient for full mixing. [11] Positive ions emanate from the ion source when it is biased at a positive voltage, and they consist of water proton clusters due to the presence of small amounts of water. NH3 was detected by reacting it with water proton clusters: NH3 þ H3 Oþ ðH2 OÞn ! NHþ 4 ðH2 OÞm þ ðn  mÞH2 O:

ð3aÞ

This reaction is known to be fast (k2 = 2  109 cm3 s1) for n up to 9 [Viggiano et al., 1988]. It is likely to proceed at significant rates for n even larger. Note the products of equation (3a) are difficult to assign, and thus they are ambiguously written as some stripping of water molecules from the core NH4+ ion may occur during sampling. In our system with a typical electric field of 300 V cm1 the mean ion energy is essentially the same as the gas temperature and the proton water clusters are dominated by values of n between 4 and 7 [Lau et al., 1982]. Therefore a rate coefficient of 2  109 cm3 s1 was used to calculate the approximate ammonia concentrations from ½NH3 ¼ lnð1 þ SNH4þ =SH3Oþ Þ=k3 t;

ð3bÞ

where the ions signals Si are the sum of all i species plus associated water clusters and t is the ion molecule reaction time (varies from 0.003 to 0.015 s) and is given by t ¼ l 2 =ðmV Þ;

ð4Þ

where l is the distance and V is the voltage difference between the source and mass spectrometer inlet (3.5 cm and 500 to 2500 V, respectively), and m is the mobility of the reactant ion which is estimated to be 2.1 cm2(sV)1 at 0.8 atm and 275 K for the n = 5 proton cluster (see the appendix). A typical value of the ‘‘measured’’ NH3 level from (3) is [NH3] = 1.2  109 cm3 (i.e., 55 pptv at 610 torr and 275 K, nN2 = 2.14  1019 cm3) for a typical NH3 addition (50 ppbv in 30 sccm, i.e., a fully mixed, average NH3 level of 100 pptv). Measured NH3 levels were typically half of that calculated assuming full mixing, and this is probably due to loss on the flow tube wall and other surfaces. In the appendix, we estimate an uncertainty of +50/35% in the reported NH3 and H2SO4 concentrations. 2.2. Computational Fluid Dynamics [12] The mixing of ammonia into the main flow and NH3 loss to the flow reactor wall was evaluated with a computational fluid dynamics (CFD) model. Information about the flow and temperature fields is also obtained. A portion of

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the cold region (275 K) of the flow reactor 50 cm long by 10 cm inner diameter was modeled. The aluminum heat exchanger was not explicitly modeled, and thus the temperature of the incoming N2 carrier gas was set at a temperature of 285 K (this is the approximate temperature of the gas just below the heat exchanger measured with a thermocouple). The ammonia inlet was located 23 cm from the main flow inlet, and ammonia was introduced at a level of 16 ppbv in the 30 sccm flow, which would result in an average [NH3] of 33 pptv. NH3 was assumed to be lost from the gas phase upon each collision with a surface. In the interest of maintaining simplicity, we did not include the mass spectrometer inlet or ion source in the model. Note that these simulations are not expected to yield results that are crucial to the interpretation of our data. They are considered to be illustrative and will provide supporting evidence for that interpretation. [13] The results of this simulation show that after the 25 cm of travel from the NH3 inlet to the detection region, the ammonia has spread out over a significant portion of the flow reactor radial cross section. Figure 1 shows contour plots of the distribution of ammonia on an axial cross section (Figure 1a) and at the level of the detection region (Figure 1b). In Figure 1a it can be seen that [ NH3] takes maximum values of 90, 50, 35, 30, and 25 pptv at distances of 20, 15, 10, 5, and 0 cm above the detection region, respectively. The decreasing [NH3] down the flow reactor reflects the loss of NH3 to the flow reactor wall. The maximum ammonia concentration in the detection region in Figure 1b is 75% of that calculated assuming full mixing with no losses. This value was very sensitive to the value of the diffusion coefficient selected for NH3 in N2 (we used 0.2 cm2 s1). This, along with the provisions discussed above, lead us to expect only qualitative agreement with the measurements where ammonia was 50% of the calculated average ammonia. [14] The ion source, the mass spectrometer inlet, and the CDC are schematically shown in Figure 1b. Qa is a flow of clean, dry N2 that is introduced on the high-pressure side of the orifice. It is meant to minimize the amount of water vapor that enters the vacuum system and is typically set such that there is excess flow of the order of 50 to 100% of that which enters the vacuum system (90 sccm). The ions formed in the ionization region traverse this region due to the 100-V potential between the first plate and the orifice. Below we present evidence that the excess Qa flow also interacts with the neutral clusters, drying them out of NH3 and probably H2O molecules. 2.3. Ionization Processes [15] The production of ions from neutral clusters via equation (2) has a linear time dependence. Therefore the ratio of the signals of any two ions produced via direct ionization of neutral clusters is independent of ion reaction time. We use the signal due to H2SO4, the HSO4 ion, to scale (ratio) the other ion signals because the signal due to H2SO4 cannot be due to ion-molecule association reactions. In addition, scaling an ion signal to HSO4, (1&0, 0), takes into account the changes in sampling efficiency that occur as the ion reaction time is varied. It is possible that ionization of H2SO4 NH3 would lead to HSO4; however, its presence is thought to be very low ( 3 in either spectrum; thus this subtraction process did not mask the detection of these clusters. The signals for 195 amu (H2SO4 dimer) and 293 amu (H2SO4 trimer) were obtained from the measured signals by subtracting the estimates of the signal due to ion-molecule clustering reactions such as equation (5a). Note that the ions at 195 and 293 amu are likely due to ionization of neutral clusters that contain NH3 in addition to the neat (H2SO4)2,3 species. The trimer, tetramer, pentamer, and hexamer of sulfuric acid along with an assortment of NH3 ligands are readily observed in the data. It is apparent that the ion signals for successive HSO4(H2SO4)n1(NH3)m species are comparable, and thus they are due primarily to ionization of pre-existing neutral clusters. Further evidence for this is the time independence of these signals, which is demonstrated in Figures 4 and 5 below. The solid designator lines represent the mass for the nth –mer of H2SO4 along with m = 0 to n NH3 molecules. The dashed lines indicate an HNO3 ligand that may arise during the ionization and transport processes. [24] Note that there are peaks in Figure 2 that correspond to the binding of an HNO3 molecule to the ions for the trimer plus NH3 ligands. For the sake of clarity, it is fortunate that the (H2SO4)4,5 clusters do not appear to exhibit this behavior. The trimer data are also complicated by unidentified impurities that result in mass peaks with

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Figure 2. Mass spectrum at 265 K revealing the presence of (H2SO4)m( NH3)n clusters. Solid lines indictate (n, m) with the ticks indicating the number of NH3 molecules (m = 0 to n). The dashed lines indicate these same clusters but with an HNO3 ligand attached. Reactant concentrations: 90 pptv H2SO4 and 180 pptv NH3. intensities of 10 Hz at 308, 312, and 356 amu. These were highly variable and did not depend on the presence of H 2 SO 4 or NH3 . The ion signal at 310 amu, due to (H2SO4)3NH3, is strongly affected by these impurities and the subtraction process leads to an oddly shaped peak, as seen in Figure 2, and at times leads to a highly uncertain signal level. This general trend that an ion holds onto HNO3 ligands more strongly the smaller it gets is opposite to the trend for H2O and NH3. This is consistent with previous studies of the association of HNO3 with negative ions [Davidson et al., 1977; Viggiano et al., 1982]. [25] The signals for the hexamer and heptamer are in general lower than those for the tetramer and pentamer. Also, the distribution of ammonia ligands is less uniform than the (H2SO4)4,5 clusters. We may be detecting the hexamer and heptamer clusters less efficiently than the smaller clusters if a majority of the hexamer and heptamer neutral clusters are present as (H2SO4)n(NH3)m where m  n. In fact, the data presented in Figure 2 show no indication of the ions HSO 4(H 2 SO 4 ) m (NH 3 ) m+1 , designated in shorthand as (1&m, m + 1), for all m. We present evidence below that these types of clusters might not be as easily ionized as the case where m < n.

[26] Water molecule ligands are not generally observed in the mass spectrums (with the possible exception of the H2SO4 hexamer and heptamer umbrellas.) This was also the case in our previous work at 240 K in the H2SO4-H2O system [Eisele and Hanson, 2000]. The CDC chamber, however, was at a lower pressure in this work, and some water ligands might be expected to survive into the mass filter as the ions experience less collisions. A mass spectrum in the H2SO4-H2O system was taken at 243 K with the current low CDC pressure and is presented in Figure 3. A mass spectrum taken at a lower [H2SO4] (40% of that for the other experiment) is also shown. H2O ligands are bound strongly enough by the pentamer and hexamer cluster ions to be clearly observed. This is not the case for the smaller H2SO4 cluster ions (note the H2SO4 trimer ion signals have been divided by 4.) It is likely that all the neutral clusters contain H2O molecules at this RH (60%) because they depend on the presence of H2O as was discussed previously [Eisele and Hanson, 2000]. Also, the monomer likely picks up one H2O at 10% RH and a second around 50% RH [Hanson and Eisele, 2000]. Apparently, small cluster ions do not hold onto ligands that were associated with the neutral cluster as well as those produced from large clusters. These

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Figure 3. Mass spectrum at 243 K taken in the absence of ammonia showing waters of hydration on the (H2SO4)m clusters (110 pptv, [H2SO4] = 2.8  109 cm3). A second mass spectrum is also shown taken with a much lower [H2SO4] (1.2  109 cm3.) Solid lines indicate the number of H2O molecules in the cluster. Note the change in scale for the signals for masses of 380 amu and less. data indicate the low pressure in the CDC will allow for some preservation of the ligands on cluster ions, which is one of the goals of this work. Note that the preservation of H2O ligands in this mass spectrum probably reflects the stability of the ion + ligand at this temperature. At the warmer temperatures in the ammonia cluster studies, however, we might not expect H2O ligands to remain on the ions. 3.1. Ion Processes [27] Figure 4 shows the ion signals (divided by the monomer signal) versus ion drift time for dimer plus ligands (Figure 4a), trimer plus ligands (Figure 4b), and tetramer plus ligands (Figure 4c). The temperature was 265 K, H2SO4 was at 50 pptv, and NH3 was at 230 pptv. Not shown are the pentamer + NH3 ligands, which were comparable in signal levels to those of the tetramer. A plot of this ratio for a particular ion will be flat if it is due to a neutral cluster and if the product ion is stable for times of the order of 0.02 s. The ions HSO4(H2SO4)m(NH3)n for m = 1, 2, 3 we will denote in shorthand as dimer, trimer, and tetramer of H2SO4 for all n. There are a few ions for n = 1 and 2 that contain an HNO3 ligand. Note that in Figure 4a the 195 amu ion signal has been divided by 10. Twice the slope of this line divided by the measured monomer concentration of 1.1  109 cm3 yields a value of 1.7  109 cm3 s1 for the association rate coefficient for H2SO4 + HSO4 ! HSO4(H2SO4) at 265 K. This is close to the value of 1.4  109 cm3 s1 at 240 K [Eisele and Hanson, 2000] (this previously reported value has been revised according to a detailed treatment of the ion mobility; see the appendix.) Note that the signals at 212 and 275 amu decrease with reaction time, indicating that they may be decomposing. Their contribution to the 195 amu ion is minimal (remember the 195 signal ratio has been divided by 10.) [28] In Figure 4b the trimer plus ligand signals at 310, 327, and 390 amu decrease with time indicating that they are losing NH3 and HNO3 as the ion drift time is increased. The slope of the 293 signal divided by estimated [dimer] (obtained from the intercept in Figure 4a) yields a value for the clustering rate coefficient of 108 cm3 s1. This is an unrealistic value and points to an increase with time of the 293 amu signal as the 310 (and 327 and 390) amu ions lose

ligands. Evidence for this is seen in the sum of these ion ratios, also shown in Figure 4b, which is constant with time within the scatter. In Figure 4c the ion signals for the tetramer do not show decomposition behavior. [29] Figure 5 shows the results for clusters up to the pentamer at 275 K with higher [reagent] present: [H2SO4] = 2.65  109 cm3 (120 pptv) and [NH3 ] = 6  109 cm3 (280 pptv). In this case, the dimer and trimer ions, HSO4H2SO4 and HSO4(H2SO4)2, do not have ligands associated with them to a significant extent. Apparently, the decomposition rates are too fast to allow them to be observed if they are sampled at times 3 ms. The association rate constant (e.g., reaction (5a)) obtained from the slope of the 195 amu ion signal versus time from Figure 5a is 2.4  109 cm3 s1. This is higher than the values found at lower temperatures. A rate coefficient this large at 275 K is consistent with results from other experiments conducted without ammonia and at lower [H2SO4] with and without ammonia (values for k1,2 ranged from 2.2– 2.6  109 cm3 s1.) A 40% increase in the ion-molecule association rate coefficient as the temperature is increased from 265 to 275 K is unexpected. Further experimentation is needed to fully understand this. [30] At this temperature the ions for the tetramer and pentamer show decomposition. The HSO4(H2SO4)3(NH3)3 ion at 442 amu, denoted shorthand as (1&3, 3), decreased by 50% as the ion time increased from 3 to 10 ms. This is consistent with a lifetime of 10 ms. The (1&4, 4) ion at 557 amu decreases by 30% as the ion time increases from 3 to 10 ms resulting in a lifetime of 25 ms. While a decrease in the (1&3, 2) ion at 425 amu and an increase in the (1&3, 1) ion at 408 amu are apparent, the lifetimes of these ions are not easily estimated owing to there concomitant production. See the appendix for an example of measuring decomposition rates of the NO3(HNO3)2 ion with this system. [31] The decomposition times observed here are in the ballpark of the 5 ms estimate from the measurements by K. Froyd and E. R. Lovejoy (private communication, 2001) discussed above. The uncertainty in this estimate of the lifetime is high and is due to the uncertainty in G and in the association rate constant (a value of 1  109 cm3 s1

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Figure 4. Ion signals due to molecular clusters (ratioed to the monomer signal) versus ion drift time at 265 K: (a) H2SO4 dimer + NH3 and HNO3 ligands (195 amu signal is shown divided by 10), (b) trimer + ligands, (c) tetramer + ligands. The [H2SO4] was 1.1  109 cm3 and [NH3] was 5  109 cm3. was assumed for the high-pressure limit.) Note that a ±0.5 kcal mol1 uncertainty in the measured G translates into a factor of +150/60% uncertainty in the lifetime at 298 K. Extrapolation to 275 K introduces an additional /1.33 factor in the uncertainty of the lifetime for a ±2 kcal mol1 uncertainty in the enthalpy. Thus the 5 ms lifetime has an uncertainty of +200/70% if G at 298 K is known to within 0.5 kcal/mol. The uncertainty due to estimating the association rate coefficient is likely to be of the order of a factor of 2. Considering these uncertainties, the 10 to 25 ms lifetimes we extract from the data are consistent with those inferred from previous observations. [32] Finally, the scatter in the data taken at 265 K is quite large, e.g., the 442 amu ion in Figure 4c. This could

be due to convectively driven processes in the flow that affect mixing. A nonsteady flow due to convective processes might be expected due to the cooling of the gas. Note the ion signals at 275 K do not have as much scatter, consistent with a more steady flow profile due to less convection. A difference in H2SO4 profiles in the detection region at 265 and 275 K might also arise. This difference may partially explain the anomolous temperature dependence of the ion-molecule association rate coefficient discussed above. 3.2. Effect of Dilution Flow on Molecular Clusters [33] In each of the distributions within a cluster the absence of signal directly attributable to the (H2SO4)n(NH3)n

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Figure 5. Ion signals due to molecular clusters (ratioed to the monomer signal) versus ion drift time at 275 K: (a) dimer (divided by 10) and trimer + ligands, (b) tetramer + ligands, (c) pentamer + ligands. [H2SO4] was 2.65  109 cm3 and [NH3] was 6  109 cm3.

cluster is clear. This may be due to loss of NH3 ligands upon ionization by NO3 core ions as discussed above. It could also be due in part to less efficient ionization of these types of clusters by NO3. As alluded to earlier, there is evidence that the neutral clusters that contain as many NH3 molecules as H2SO4 molecules may not be easily ionized. We discovered this by observing that the cluster ion signals went through a maximum when there was an outflow of dry N2 from the mass spectrometer inlet into the main flow. As outlined in Figure1b the mass spectrometer inlet has a 0.20-inch ID aperture on the front plate through which the ions pass before entering a 125-mm orifice (mounted on the orifice plate) through which they enter the vacuum system. A flow of dry N2, labeled Qa in Figure 1b, between these plates limits the amount of water that enters the vacuum system. Excess Qa that does not enter the vacuum system enters the flow reactor. [34] The results of these tests are shown in Figure 6, a plot of the ion signals divided by the signal due to H2SO4 (except for the HSO4 signal itself which is presented as ln(1 + SHSO4/SNO3)) versus the flow rate of gas added at

the inlet Qa. The flow entering the mass spectrometer through the 125 mm orifice at 0.8 atm is 90 sccm; any flow in addition to this enters the main flow. An arrow in the figure indicates this point along the X axis. The temperature was 265 K, while NH3 was 130 pptv and H2SO4 was 70 pptv. For some of the (H2SO4)n clusters the ion signals were summed: for the tetramer, the sum of 408, 425, and 442 amu; and for the pentamer, the sum of 540 and 557 amu. An additional experiment with much more ammonia, 780 pptv, present is also included in Figure 6. Also shown as the gray symbols and curve is the ratio of 442 amu/408 amu (divided by 1000). [35] Note the marked increase in the ion signals due to clusters when Qa exceeds the inlet flow. At the maximum effect where Qa is 55 sccm in excess, the cluster ion signals increase by multiplicative factors of 2 – 3 over the signals at the lowest Qa. Also, at the high [NH3] level, the pentamer signal increases by a factor of 5. The signals due to the monomer and the dimer shown in Figure 6a show little if any effect indicating there is not a large distortion in the gas or reagent ion concentration in the main flow due to Qa.

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HANSON AND EISELE: PRENUCLEATION MOLECULAR CLUSTERS

Figure 6. Ion ratios versus aperture flow rate at 265 K: (a) ln(1 + [HSO4]/ [NO3]) and dimer/monomer, (b) sum of the trimer + ligands signals, sum of the tetramer + ligands signals, sum of the pentamer with 3 and 4 NH3 ligands, and the ratio of (4, 3) to (4, 1) divided by 1000 are shown. A set of pentamer signals with much higher NH3 present is also shown. An experiment at 275 K with [NH3] at 270 pptv and [H2SO4] at120 ptv shows a much smaller peak in the cluster ion signals at Qa = 150 sccm. The maximum effect at 275 K for the trimer ion signal was +50%, while the signals due to the tetramer and pentamer (including 506 and 523 amu) both increased by 75%. [36] A possible explanation for these observations is that the excess flow acted to ‘‘dry out’’ the flow in the detection region, causing neutral clusters to lose NH3 and thus become amenable to ionization by NO3. The decrease in the cluster ions as the flow exceeded this critical value is probably due to sufficient dilution of the flow such that the clusters fall apart (i.e., defined here as loss of H2SO4) due to inadequate amounts of ammonia. This explanation is consistent with our observations that the effect increases as NH3 increases and that it decreases as temperature increases. Also shown in Figure 6b is the ratio of 442 to 408 amu ions, the (1&3, 3) to (1&3, 1) ratio, which we assign as the ratio of the 3 ammonia tetramer to the 1 ammonia tetramer. It decreases as Qa increases, indicating a change in the neutral distribution due to this excess flow (note these ions are stable at 265 K on timescales of many tens of milliseconds as shown in Figure 4).

[37] Because the excess Qa flow is

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