Thermodynamics of the formation of sulfuric acid dimers in the binary (H2SO4-H2O) and ternary (H2SO4-H2O-NH3) system

A. Kürten, S. Münch, L. Rondo, F. Bianchi , J. Duplissy, T. Jokinen, H. Junninen , N. Sarnela , S. Schobesberger , M. Simon, M. Sipilä, J. Almeida, A. Amorim, J. Dommen , N. M. Donahue , 5 E. M. Dunne, R.C. Flagan , A. Franchin, J. Kirkby, A. Kupc, V. Makhmutov, T. Petäjä, A. P. Praplan, F. Riccobono , G. Steiner , A. Tomé, G. Tsagkogeorgas , P. E. Wagner , D. Wimmer, U. Baltensperger , M. Kulmala, D. R. Worsnop , and J. Curtius 1


INTRODUCTION
The formation of new particles from the gas phase is a frequent and important process in the atmosphere. Substantial progress has been made in recent years describing the chemical systems and the mechanisms that could potentially be relevant to atmospheric new particle formation (NPF). Observed atmospheric 5 boundary-layer nucleation rates typically correlate with the concentration of gaseous sulfuric acid (Kulmala et al., 2004;Kuang et al., 2008). Moreover, it is generally accepted that the presence of water vapor enhances nucleation in the binary (H2SO4-H2O) system. However, nucleation under typical ground-level conditions cannot be explained by the binary nucleation of sulfuric acid and water vapor (Kulmala et al., 2004;Kerminen et al., 2010), even if the enhancing effect due to ions is taken into 10 account (Kirkby et al., 2011). Therefore, assuming that sulfuric acid is required for nucleation, at least one additional compound is necessary to stabilize the nucleating clusters (Zhang et al., 2012). Ammonia, amines and highly-oxidized organic compounds have been identified in ambient samples or tested in laboratory experiments (Ball et al., 1999;Hanson and Eisele, 2002;Chen et al., 2012;. Recent chamber experiments showed that the observed atmospheric boundary layer nucleation 15 rates can, in principle, be explained by sulfuric acid acting in combination with either amines or the oxidation products from α-pinene (Almeida et al., 2013;Schobesberger et al., 2013;Riccobono et al., 2014).
Nucleation has also frequently been observed in the free troposphere, where the temperature and gas mixture differ from those at the surface (Brock et al., 1995;Weber et al., 1995;Clarke et al., 1999;Lee 20 et al., 2003). An important source for stratospheric particles is the tropical tropopause region where nucleation mode particles have been observed. Additionally, new particle formation has also been observed in the free troposphere (Brock et al., 1995;Clarke et al., 1999;Borrmann et al., 2010;Weigel et al., 2011). Due to the volatility and the identification of sulfur in collected particles it was concluded that binary nucleation contributes to (or dominates) the formation of these particles (Brock et al., 1995).
Binary homogenous nucleation also seems to play an important role in forming the mid-stratospheric condensation nuclei layer, although ion-induced binary nucleation cannot be ruled-out (Campbell and Deshler, 2014). Several studies provide evidence that ion-induced nucleation may be an important process in the free troposphere (Lee et al., 2003;Lovejoy et al., 2004;Kanawade and Tripathi, 2006;Weigel et al., 2011). These studies suggest that binary nucleation is important on a global scaleespecially in regions where very low temperatures prevail, and where the concentrations of stabilizing substances involved in ternary nucleation are low.
Nucleation in the binary system starts with the collision of two hydrated sulfuric acid monomers, which form a dimer . In this study, the notation "dimer" refers to a cluster that contains two sulfuric acid molecules plus an unknown amount of water and, in the ternary system, 35 ammonia. The term monomer refers to clusters with one sulfuric acid, irrespective of whether the cluster contains also ammonia and/or water molecules or not. Unless stated otherwise the terms "monomer" and "dimer" describe the neutral, i.e., uncharged molecules and clusters. The probability that a dimer will or will not grow larger depends on its evaporation rate as well as its collision rate with monomers and larger clusters. Therefore, it is crucial to know the evaporation rate (or the equilibrium constant) of the sulfuric acid dimer in order to understand and model binary nucleation. Hanson and Lovejoy (2006) measured the dimer equilibrium constant over a temperature range of 232 to 255 K. However, no direct 5 measurements have been performed for lower temperatures. Moreover, evidence exists that ammonia is an important trace gas influencing new particle formation in some regions of the atmosphere (Weber et al., 1998;Chen et al., 2012). Numerous studies using quantum chemical calculations have been conducted to study the cluster thermodynamics for the sulfuric acid-ammonia system (Kurtén et al., 2007;Nadykto and Yu, 2007;Torpo et al., 2007;Ortega et al., 2012;Chon et al., 2014). To our 10 knowledge, however, only very few studies have yet reported experimentally determined dimer concentrations for this system (Hanson and Eisele, 2002;Jen et al., 2014). In order to model NPF for the ternary system involving ammonia it is essential to better understand the thermodynamics of the clusters involved in the nucleation process. Cluster properties derived from measurements can be used for a comparison with the theoretical studies. Such a comparison provides a consistency check for both 15 the models and the measurements.
Here we present experimentally derived dimer evaporation rates for the binary system (H2SO4-H2O) at temperatures of 208 and 223 K. The measurements of the sulfuric acid monomer and dimer were made with a Chemical Ionization Mass Spectrometer (CIMS) at the Cosmics Leaving OUtdoor Droplets (CLOUD) chamber. The data are discussed and compared to previously published dimer evaporation 20 rates for the binary system (Hanson and Lovejoy, 2006). Dimer measurements are also available for the ternary system (H2SO4-H2O-NH3) at 210, 223, and 248 K and some ammonia mixing ratios (< ~10 pptv).
The thermodynamics (dH and dS) of the H2SO4•NH3 cluster were retrieved from comparison of the measured monomer and dimer concentrations with those predicted using a simple model. Furthermore, neutral cluster measurements using Chemical Ionization-Atmospheric Pressure interface-Time Of Flight 25 (CI-APi-TOF) mass spectrometry are presented for the binary system at 206 K for clusters containing up to 10 sulfuric acid molecules.

CLOUD chamber
CIMS monomer and dimer measurements were conducted primarily during the CLOUD5 campaign in October and November 2011. Additional CI-APi-TOF measurements were made during one experiment 35 in November 2012 (CLOUD7). The CLOUD chamber has been described in previous publications (Kirkby et al., 2011;Almeida et al. 2013;Riccobono et al., 2014). The 26.1 m 3 electropolished stainless-steel chamber provides an ultra-clean environment for studying new particle formation and growth. A well-insulated thermal housing and temperature control allow measurements down to 193 K with a stability of a few hundredth of a degree. For cleaning purposes the chamber can be heated up to 373 K and flushed with ultra-clean air at a high ozone concentration. Pure neutral nucleation was studied by applying a high voltage (±30 kV) to upper and lower transparent field cage electrodes (termed clearing 5 field high voltage or CFHV in the following). Sampling ports are located around the mid-plane of the cylindrical chamber, where the clearing field is at 0 V. Grounding the electrodes allows measurements of ion-induced nucleation. In the absence of a clearing field galactic cosmic rays produce ion pairs at a rate of ~2 cm -3 s -1 ). Much higher ion pair production rates can be achieved by illuminating a section of the chamber (approximately 1.5 m times 1.5 m) using a defocused pion beam from CERN's proton synchrotron (Duplissy et al., 2010). Ultra-clean gas is provided to the chamber by mixing nitrogen and oxygen from cryogenic liquids at a ratio of 79:21. Different relative humidities (RH) can be achieved by passing a portion of the dry air through a nafion humidification system. The temperature and the dew/frost point inside the chamber are monitored continuously; the RH is calculated using the equations given by Murphy and Koop (2005). A fibre optic system (Kupc et al., 2011) feeds UV light into the 15 chamber, which initiates the photolytic production of sulfuric acid when H2O, O2, O3, and SO2 are present. Two mixing fans continuously stir the air inside the chamber assuring its homogeneity (Voigtländer et al., 2011).
The CLOUD5 campaign was dedicated to experiments investigating new particle formation at low temperatures (down to ~208 K) for the binary (H2SO4-H2O) and the ternary (H2SO4-H2O-NH3) systems.

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The particle formation rates at low temperature will be reported in forthcoming papers; this publication focuses on measurements of the sulfuric acid monomer and the sulfuric acid dimer. One future paper will also focus on the determination of the ammonia mixing ratios at the low temperatures. These were evaluated from a careful characterization of the CLOUD gas system, which delivers ammonia diluted in ultra-clean nitrogen and air to the CLOUD chamber. The gas system was characterized by 25 measurements with a LOng Path Absorption Photometer (LOPAP, Bianchi et al., 2012), an Ion Chromatograph (IC, Praplan et al., 2012) and a Proton Transfer Reaction-Mass Spectrometer (PTR-MS, Norman et al., 2007). Table 1 gives an overview over the main findings relevant to this study obtained from the two different campaigns.

Pressure interface-Time Of Flight (CI-APi-TOF) mass spectrometer
During CLOUD5 a CIMS was used for the measurement of sulfuric acid monomers and dimers (Kürten et al., 2011). Using nitrate ions NO3 -(HNO3)x=0-2, sulfuric acid can be selectively ionized; detection limits below 10 5 cm -3 (referring to the monomer of sulfuric acid) can be reached for short integration times, thereby enabling high time resolution (Eisele and Tanner, 1993;Mauldin et al., 1999;Berresheim et al., 2000). The instrument was calibrated before and after the campaign using a system that produces a known concentration of sulfuric acid (Kürten et al., 2012). In this way, the recorded ion signals -for the primary ions and the reactant ions -can be converted into a concentration of sulfuric acid.
The compound X is, in most cases, water, but in the case of the ternary system, both experiments and 10 quantum chemical calculations suggest that dimers could also be bound to ammonia (Hanson and Eisele, 2002;Kurtén et al., 2007). Ammonia (or X) is expected to evaporate rapidly after the ionization . It should be noted here that even if X did not evaporate after the ionization it would probably be removed in the CIMS collision dissociation chamber (CDC). In the CDC any remaining water molecules are stripped off from the core ions and the NO3 -(HNO3)0-2 ions yield mostly NO3due 15 to the declustering. Therefore, the monomer and dimer sulfuric acid concentrations are estimated to be: Here, CR denotes the count rate for the primary ions (CR62 at m/z 62 for NO3 -), the HSO4ions (CR 97 at m/z 97), and the HSO4 -(H2SO4) ions (CR 195 at m/z 195), respectively. The constant C is derived from a 20 calibration and has been evaluated as 1.1x10 10 cm -3 with a typical uncertainty of ~30% (Kürten et al., 2012). The same calibration constant is used for the monomer and the dimer because it is not possible to calibrate the dimer signal. Since both H2SO4 and (H2SO4)2 are thought to react with the nitrate ions at the collision limit this assumption is well justified. The factors Lmonomer and Ldimer take into account the penetration through the sampling line from the CLOUD chamber to the CIMS ion source. A sample 25 flow rate of 7.6 standard liters per minute (slm) and a sampling line length of 100 cm were used to calculate the transmission. The diffusion coefficient has been calculated for the respective temperature and RH for the monomer from the data given by Hanson and Eisele (2000). It was assumed that the diffusivity of the hydrated dimer (see Henschel et al., 2012) equals 0.06±0.01 cm 2 s -1 at 298 K, and varies with temperature as (298K/T) 1.75 .
by the CIMS. However, during CLOUD7 it was not possible to measure the dimers with the CIMS due to instrumental problems. The CI-APi-TOF has an almost identical chemical ionization source as the CIMS but it uses a time of flight mass spectrometer with high mass resolution (around 4500 Th/Th) and mass accuracy (better than 10 ppm). These features as well as the wide mass range (up to around 2000 Th) enable detection and unambiguous identification of the elemental composition of clusters. As will 5 be shown in Section 3.4 neutral clusters containing as many as 10 sulfuric acid molecules were detected during a binary experiment at 206 K.

10
As it is not possible to calibrate the CIMS or the CI-APi-TOF with a known concentration of sulfuric

15
and H2SO4 within the CIMS ion drift tube (Hanson and Eisele, 2002). The estimated dimer count rate through this process is (Zhao et al., 2010;Chen et al., 2012) The reaction time treact is approximately 50 ms in our case (Kürten et al., 2012). A value of 8x10 -10 cm 3 s -1 was used for k21, the rate constant for reaction between HSO4and H2SO4 (Zhao et al., 2010). The 20 measured count rate CR195 was compared to the expected count rate during a calibration in which a high concentration of sulfuric acid monomers was presented to the CIMS. From this comparison, we concluded that the dimer signal is suppressed by a factor of 1.2 relative to the monomer signal. The discrepancy can either be due to mass discrimination or due to some fragmentation in the CIMS CDC.
In any case, it means that the measured dimer signal needs to be multiplied by a factor of 1.2 (with an 25 estimated statistical uncertainty of less than 10%) when its concentration is evaluated.
The background signal, e.g., from electronic noise, is always subtracted before the dimer concentration is evaluated according to equation (1b). The background was obtained by averaging over a certain period just before the experiment started, i.e., before the UV lights were turned on and the H2SO4 was produced. In addition to the background, the contribution from IIC is subtracted from the 30 dimer signal (Chen et al., 2012). This effect becomes relevant at about 1x10 7 cm -3 for the sulfuric acid monomer under the conditions of this study.

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The goal of this study is to determine sulfuric acid dimer evaporation rates from data obtained by monomer and dimer measurements. In order to derive a formula for the evaporation rate it is useful to start with the basic equations governing the loss and the production of the clusters. Since low temperature conditions (208 and 223 K for the binary system) are considered in this study the assumption is made that only the smallest clusters (dimer and trimer) have appreciable evaporation rates (Hanson and Eisele, 2006 where Ni is the concentration of the cluster containing i sulfuric acid molecules. The evaporation rate ki,e refers to the evaporation of one sulfuric acid molecule from a cluster containing i sulfuric acid molecules. In a chamber experiment such as CLOUD, three loss processes are relevant for neutral particles; these include the wall loss rate ki,w, the dilution rate kdil through the replenishment of the chamber air (independent of particle size), and coagulation with the coefficient Ki,j describing collisions 10 between the clusters i and j. The factor Gi,j represents an enhancement in the collision rates due to dipoledipole interactions (McMurry, 1980;Chan and Mozurkevich, 2001). In order to derive an expression for the dimer evaporation rate, we assume steady-state (dN2/dt = 0). Equation (3) can then be written as It is useful to estimate the relative importance of the three terms on the right-hand side of equation (4).

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The numerator in the first term describes the production rate of dimers from monomers. The collision constant for two monomers is approximately 2.8x10 -10 cm 3 s -1 at 208 K. If the enhancement factor G due to dipole-dipole interactions is included, this value is ~6.9x10 -10 cm 3 s -1 (McMurry, 1980;Chan and Mozurkevich, 2001). As an example, at 208 K under binary conditions, the smallest monomer concentration evaluated is 2x10 6 cm -3 , at which point the dimer was evaluated as 1x10 4 cm -3 (Section 20 3.3). These values yield 0.2 s -1 for the first term. The second term is significantly smaller than the first term, so it can be neglected due to the reasons listed in the following. The trimer concentration (although it was not measured) should be smaller than the dimer concentration because the trimer is produced from the dimer. Moreover, the trimer evaporation rate is expected to be lower than the dimer evaporation rate (e.g., 1.6x10 -3 s -1 for the trimer, and 0.3 s -1 for the dimer at 208 K and 20% RH, see Hanson and Lovejoy, 25 2006). The third term includes losses due to walls, dilution, and coagulation. The wall loss rate for a dimer is approximately 1.5x10 -3 s -1 , while loss due to dilution is ~1x10 -4 s -1 . The loss due to coagulation depends on the particle size distribution, and can be important when the dimer evaporation rate is small. Loss of dimers due to collisions with monomers (i.e., growth to form trimers) then dominates the coagulation term, which is usually on the order of 10 -2 s -1 (e.g. N1 = 1x10 7 cm -3 and 30 G1,1•K1,1 = 6.9x10 -10 cm 3 s -1 ). All elements of the third term are, thus, small compared with the first term, and so these can also be neglected. For the conditions of this study, consistent with the extrapolated data by Hanson and Lovejoy (2006), the evaporation rates are however larger than 10 -2 s -1 . This means that evaporation dominates over the other losses; therefore, k2,e can be approximated by The concentrations used in equation (5) are averages over periods where conditions are close to steadystate. These periods are defined by conditions where the production and loss rates for the dimer and the monomer are almost identical and the concentrations are not subject to significant changes anymore. If losses by processes other than evaporation were not negligible, retrieval of evaporation rates would require use of a numeric model that also includes larger clusters since coagulation loss depends on 5 concentrations of all other clusters. Nevertheless, model calculations simulating cluster and particle concentrations are needed to evaluate other effects relevant to this study, as will be discussed in the next sections.
Comparison of the rate constants used for the reactions between HSO4and H2SO4 (Section 2.3) and between H2SO4 and H2SO4 yields that the neutral-neutral collision rate is about the same as the charged-10 neutral collision rate. This is due to the relatively large enhancement factor from dipole-dipole interactions for the neutral-neutral rates (McMurry, 1980;Chan and Mozurkevich, 2001) and the observation that the reaction between the bisulfate ion and sulfuric acid seems not to proceed at the collisional rate (Zhao et al., 2010). We have no mechanistic explanation why the formation of HSO4 -(H2SO4) should proceed at a rate slower than the collision rate. Comparison with similar ion-molecule 15 reactions shows, e.g., that the formation of NO3 -(H2SO4) proceeds at the collision rate (Viggiano et al., 1997), whereas this does not seem to be the case for the formation of NO3 -(HNO3) (Viggiano et al., 1985). Uncertainties regarding the rate of formation for the HSO4 -(H2SO4) cluster remain and these have to be addressed in future studies. Further discussion about the consequences this uncertainty has on the present study is provided in Section 3.8.

SAWNUC model
The Sulfuric Acid Water NUCleation model (SAWNUC) of Lovejoy et al. (2004) simulates ion-induced nucleation in the binary system. Cluster growth is treated explicitly by a step-by-step addition of sulfuric 25 acid molecules while equilibrium with water molecules is assumed due to the relatively high concentration and evaporation rate of H2O compared to H2SO4. SAWNUC takes into account sulfuric acid condensation and evaporation, coagulation, and losses due to walls and dilution (Ehrhart and Curtius, 2013). In SAWNUC, evaporation rates of small, negatively-charged clusters are based on measured thermodynamics and partly on quantum chemical calculations Froyd and Lovejoy, 2003). More detailed information on SAWNUC can be found in Lovejoy et al. (2004), Kazil and Lovejoy (2007), and Ehrhart and Curtius (2013).
As this study focuses on neutral binary nucleation, we neglect the charged-cluster channel, and only simulate the neutral channel. Coagulation coefficients have been calculated according to Chan and Mozurkewich (2001). They quantified London-van der Waals forces (dipole-dipole interactions) for low temperatures, only dimer (and sometimes trimer) evaporation has been taken into account. The exact input parameters are specified in the following sections.

5
Previous dimer evaporation rates were evaluated with the CIMS ionization source integrated within a temperature-controlled flow tube (Hanson and Lovejoy, 2006). This set-up ensured that the temperature did not change between the times when the dimers were formed, and when they were ionized. In the present study, the dimers formed inside the CLOUD chamber, which is very precisely temperaturecontrolled. However, the monomers and dimers had to be transported from the chamber to the CIMS 10 through a 100 cm long sampling line. The first ~80 cm of this line were held at the same temperature as the chamber because it protruded through the thermal housing and into the chamber. Moreover, the sampling line was enclosed by an insulated copper tube. Since a large part of the copper volume was placed inside the thermal housing, the cold temperature was maintained over the full length of the copper tube due to efficient heat conduction even for a short section of the tube that was located outside the 15 chamber, while the insulation minimized heat transfer to the surrounding air. The CIMS ion drift tube was connected to the tip of the copper jacketed sampling line by means of a short tube that was not temperature-controlled, exposing the last 15 to 20 cm (the measured length is closer to 15 cm but to be conservative we took into account a somewhat longer distance) of the sampling line to warmer temperatures. In this region the dimers could in principle have suffered from evaporation.

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To estimate the evaporation effect, a finite difference method was used to calculate the temperature profile, as well as the dimer concentration across the sampling line over its full length. The differential equations for the monomer (i = 0) and dimer (i = 1) concentrations ci were solved as a function of the radial and axial coordinates r and z (Kürten et al., 2012): where Di is the diffusivity, Q is the flow rate and R is the radius of the tube. A parabolic flow profile was assumed and the geometry was divided into small areas in order to solve the differential equations by a finite difference method. The source terms si include evaporation and production of dimers and loss 30 and production of monomers due to self-coagulation and evaporation of dimers. Further reactions (coagulation with larger clusters/particles) were not taken into account since the time is rather short (< 1s for Q =7.5 slm, R = 0.005 m, and L = 1 m) and the other loss terms are dominant. A similar differential equation is used to determine the temperature inside the tube before the concentrations are calculated.
This temperature is used to calculate the evaporation of dimers in each of the small areas. The time- Figure 1 shows the results for a chamber temperature of 223 K. The walls of the first 80 cm of the sampling line were held at 223 K, while the last 20 cm were held at 293 K (which was a typical maximum day-time temperature in the experimental hall during the CLOUD5 campaign). It should be noted that this is an extreme case because, in reality, the temperature would slowly approach 293 K over the last 20 cm due to heat conduction along the walls of the sampling line. However, the calculations performed 5 here are used to obtain an upper-bound estimate of the error due to evaporation. The temperature of the walls is indicated by the black color (223 K) and the grey color (293 K). Figure 1 shows the normalized concentration of dimers after initializing the monomer concentration to 1x10 7 cm -3 ; the dimer was assumed to be at equilibrium initially. It was further assumed that both monomers and dimers are lost to the walls due to diffusion, and that at the same time dimers are formed due to collisions of monomers, 10 but can also evaporate. Larger clusters or particles were not taken into account. The dimer evaporation rate as a function of temperature was taken from the literature at this stage (Hanson and Lovejoy, 2006).
The profile shown in Fig. 1 indicates that, during the first 80 cm, dimers are lost primarily via diffusion because, in this section, they are essentially in equilibrium regarding formation and evaporation; only over the last 20 cm does evaporation have an appreciable effect on the dimer 15 concentration. However, only the region close to the walls of the sampling line shows a rise in the gas temperature; the center of the sample flow is essentially unaffected. The estimated overall transmission efficiency for dimers is 0.228 at a flow rate of 7.6 slm in the half-inch tube (inner diameter ~10 mm). If the temperature were held constant at 223 K over the entire tube length, the transmission would increase to 0.475 because only wall losses would take place. Since the dimer concentration is corrected for the 20 effect of diffusion loss (see equation (1b)), the additional loss factor due to evaporation would be (1/0.228)/(1/0.475) = 2.08. However, this is an upper bound estimate of the error introduced through evaporation since the temperature is, in reality, gradually changing over the last 20 cm instead of increasing as a step function as simulated. For the lower temperature of 208 K, the effect is even smaller.
From the estimations presented in this section it can, therefore be concluded that, while the sampling 25 conditions are not ideal, the maximum error introduced is very likely smaller than a factor of 2 (see also error discussion in Section 3.8). the small ion concentration is generally only on the order of a couple of thousand (Franchin et al. 2015) and the HSO4ions are not efficiently being detected by the CIMS (Rondo et al., 2014), the dimer concentration is. For the neutral conditions the dimer signal above background is due to neutral (H2SO4)2. During the GCR stage of the experiment, the dimer signal gradually increases. This could be 5 due either to neutral dimers being charged in the CIMS or charged dimer ions forming within the CLOUD chamber.

RESULTS AND DISCUSSION
Unfortunately, there was no ion filter installed in the CIMS sampling line during CLOUD5 to eliminate the ion contribution to the CIMS signal. However, evidence exists that the additional signal during GCR conditions is caused by a buildup of chamber ions rather than formation of additional 10 neutral dimers during the ion-induced experiments. Recently, it was reported that HSO4ions clustered to large oxidized organic molecules (OxOrg) can be efficiently detected by the CIMS (Rondo et al., 2014).
When both ions and sufficient H2SO4 are present in the chamber, HSO4 -(H2SO4)n with n ≥ 1 will be formed (Eisele et al., 2006); these ions are apparently being detected by the CIMS as dimers to some 15 extent. The light HSO4ions will be rapidly lost to the walls of the CIMS sampling line, whereas the larger HSO4 -(H2SO4)n≥1 ions will have a lower loss rate. Therefore, the larger ions tend to have a higher chance to survive the transport to the CIMS where they can be eventually detected as artifact dimers. If this were the case, some of the observed dimer signal from the GCR stage in Fig. 2 might not be related to the neutral dimers, and should be discarded.

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The Atmospheric Pressure interface-Time Of Flight (APi-TOF, Junninen et al., 2010) mass spectrometer measured the ion composition during the first part of the CLOUD5 campaign. Figure 2 (lower panel) shows the HSO4 -(H2SO4)n (n = 0 to 8) cluster ion signals during a binary beam experiment at 223 K. In addition, the apparent CIMS dimer concentration is displayed. The dimer signal is well correlated with the HSO4 -(H2SO4)n signal for n ≥ 5 (e.g. Pearson's correlation coefficient between the 25 dimer and the HSO4 -(H2SO4)5 signal is 0.93), indicating that the dimer signal due to ions arises mostly from larger cluster ions (hexamer and larger) which, at least partly, fragment to HSO4 -(H2SO4) before they reach the mass spectrometer. It is, however, not clear whether only the relatively large charged clusters fragment, or if only these large clusters reach the mass spectrometer due to an enhanced transmission. The study by Rondo et al. (2014) indicates that ions need to be relatively heavy (or have 30 a low enough electrical mobility) in order to reach the CIMS ion drift region. It is, therefore, also possible that ions that are smaller than the hexamer could, in principle, contribute to the CIMS dimer channel, but since they are not efficiently reaching the CIMS, their contribution is negligible. Either possibility would lead to the large charged clusters contributing to the dimer signal (Fig. 2).
Another interesting observation is that the dimer signal comes mainly from the neutral clusters when 35 ammonia is present in the chamber. Recent publications on the ternary ammonia system investigated at CLOUD showed that the APi-TOF detects HSO4 -(H2SO4)n(NH3)m with m ≥ 1 when n ≥ 3 (Kirkby et al., ammonia ion clusters are more stable than pure sulfuric acid clusters because they do not seem to fragment to the same extent. As a consequence of the observations discussed in this section, only neutral experiments were considered for the evaluation of the dimer evaporation rates in the binary system.

Effect of fragmentation during neutral experiments
In the binary system, large cluster ions can fragment and contribute to the measured dimer signal. In this section the maximum error due to the observed fragmentation described in Section 3.1 is estimated. For neutral cluster measurements, this process is, however, different from that described in the previous section. Under ion-induced conditions the ions are directly sampled from the CLOUD chamber.
Therefore, a relatively low concentration of cluster ions can contribute significantly to the dimer signal because the ionization process in the CIMS drift tube is not needed for their detection.
In a worst-case scenario all cluster ions larger than the dimer (originating from neutral clusters after ionization) would fragment and yield one HSO4 -(H2SO4) thereby increasing the apparent dimer 15 concentration. It is important to note that even a very large charged cluster could only yield one HSO4 -(H2SO4) because the clusters carry only one negative charge. The cluster concentrations (dimer and larger) can be calculated using the SAWNUC model. In any case, the cluster concentrations decrease with increasing size, so the potential contribution decreases with increasing cluster size. Figure 3 provides an upper bound estimate of the magnitude of this effect. In an example calculation for a 20 temperature of 223 K, a sulfuric acid monomer concentration of 2x10 7 cm -3 , and dimer and trimer evaporation rates from the literature (Hanson and Lovejoy, 2006) are used, while all other evaporation rates are set to zero. The model yields concentrations for the neutral dimer and all larger clusters.
Summing the concentrations from the dimer up to a certain cluster size, and normalizing the sum with the dimer concentration, yields the results shown in Fig. 3 which indicate that the contribution of the 25 larger clusters to the dimer is, at most, a factor of 3 larger than that of the dimers, even as one considers the contributions from very large clusters. Again, in this estimation it is considered that even a large

30
The estimated factor in this section is an upper limit. It is unlikely that all clusters will fragment, or that they always yield HSO4 -(H2SO4) as the product. Instead, HSO4might result from the fragmentation, because, not being an equilibrium process, fragmentation would not always yield the most stable cluster configuration. Moreover, since evaporation cools the cluster, evaporation of neutral sulfuric acid molecules from the largest clusters may be incomplete. Another argument why the data 35 from Fig. 3 provide an upper estimate is due to the reduction in transmission efficiency for the components of the mass spectrometer that is generally observed with increasing mass. In summary, the maximum effect of fragmentation is very likely on the order of a factor of 2, or lower (see also error discussion in Section 3.8).

Binary (H2SO4-H2O) dimer concentrations and evaporation rates
5 Figure  to derive even smaller evaporation rates than those observed in this study. If the evaporation rate is comparable to the other loss rates, these mechanisms need to be taken into account when estimating k2,e.
Only when the evaporation rate dominates dimer loss over the full range of [H2SO4] can other mechanisms be neglected. The neutral binary data in Fig. 4 indicate that the dimer evaporation rate varies between 0.2 s -1 for ~12 % RH and 0.04 s -1 for 58 % RH at 208 K. Therefore, relative humidity 20 has a relatively strong effect, one that is more strongly pronounced than the higher temperature (232 to 255 K) data of Hanson and Lovejoy (2006) suggest (see discussion below). Our signal-to-noise ratio was, however, not high enough to quantify the dimer at temperatures above 223 K for direct comparison.  The evaporation rates derived herein can be compared with the rates reported by Hanson and Lovejoy (2006) after some unit conversions. The equilibrium constant Keq for sulfuric acid dimer formation from 35 monomers in the presence of water has been reported as (Hanson and Lovejoy, 2006) with A = (9210±930) K, and B = 31.4±3.9 for the temperature, 232 ≤ T ≤ 255 K, and a relative humidity of 20% over supercooled water. Given the reported values for A and B the thermodynamic properties are estimated to be dH = -18.3±1.8 kcal mol -1 and dS = -39.5±7.8 cal mol -1 K -1 (Hanson and Lovejoy, 2006). Equation (7) provides the equilibrium constant in units of Pa -1 since the partial pressures p of the monomers and dimers are used. In order to calculate evaporation rates it is necessary to convert the 5 equilibrium constant to units of cm 3 , and to further apply the relationship between equilibrium constant, evaporation rate, and collision constant for the dimers (Ortega et al., 2012), leading to: where kB is the Boltzmann constant. We converted equilibrium constants reported by Hanson and Lovejoy (2006) to evaporation rates using equation (8). Hanson and Lovejoy (2006) determined 10 evaporation rates at 20% RH; while our measurements were made at different RHs. Because RH has a significant influence on the dimer evaporation further analysis is necessary to make the two data sets comparable. Figure 6 shows the evaluated dimer evaporation rates as a function of the relative humidity (with respect to supercooled water) for two different temperatures (208 and 223 K). The rates from this study 15 are based on the data shown in Figures 4 and 5 and equation (5). The data were fitted by simple power law fits and the slopes of p = -1 (at 208 K) and p = -1.6 (at 223 K) indicate that the evaporation rates decrease significantly with increasing RH. Qualitatively this is in agreement with a previous experiment (Hanson and Lovejoy, 2006) and quantum chemical calculations (Ding et al., 2003). However, Hanson and Lovejoy (2006) reported p = -0.5, where the exponent p has an uncertainty of ±100%. Our data 20 indicate a somewhat stronger influence of RH on the evaporation rates, which also seems to be dependent on temperature.
The evaporation rates from Figure 6 with RH between 10 and 30% were interpolated to 20% RH using the reported slopes. Figure 7 shows the data from this study and from Hanson and Lovejoy (2006).
Fitting the combined data set for 20% RH gives the following formulation for the equilibrium constant The black line in Fig. 7 shows the dimer evaporation rates derived from equation (9). The uncertainties in equation (9) are based on 95% confidence intervals. Overall, the two data sets are, within errors, consistent with one another, and yield dH = -20.1±1.2 kcal mol -1 and dS = -46.7±5.2 cal mol -1 K -1 . We caution that in this study the assumption is made that dH does not vary with temperature; generally this variation should, however, be small. These data are slightly different than what has been reported by Hanson and Lovejoy (2006). However, our data agree within errors with results from quantum chemical calculations, taking into account the effect of water vapor (Ding et al., 2003). According to measurements by Hanson and Eisele (2000) and quantum chemical calculations (Temelso et al., 2012;Henschel et al. 2014) the sulfuric acid monomer and dimer can contain water molecules. Therefore, the Table 2 shows a comparison between different studies dealing with the sulfuric acid dimer formation.
Regarding the effect of water vapor it should be noted that our experimentally determined evaporation rates represent an average for dimers containing different numbers of water molecules. The exact distribution of water associated with the dimers will be a function of relative humidity and temperature, which cannot be taken into account explicitly in this study. The data by Ding et al. (2003) suggest that 5 almost all sulfuric acid dimers contain four water molecules at the conditions of this study. Therefore, there exist three possibilities for a sulfuric acid monomer (H2SO4(H2O)0-2) to dissociate from the dimer with four water molecules. These reactions are listed in the last three rows of Table 2, where the evaporation rates for the monomer of sulfuric acid without water have the highest values. These are about two orders of magnitude faster than the experimentally determined values. One should note, 10 however, that the data by Temelso et al. (2012) indicate a different hydrate distribution and this will have a significant influence on the resulting effective dimer evaporation rate.

15
During the CLOUD7 campaign, experiments were conducted at ~206 K under binary conditions. In addition to the CIMS two CI-APi-TOFs were deployed (Jokinen et al., 2012;. The two instruments are labeled CI-APi-TOF-UFRA (instrument from the University of Frankfurt) and CI-APi-TOF-UHEL (instrument from the University of Helsinki). In contrast to the CIMS used during CLOUD5, the sampling lines of the CI-APi-TOFs were not temperature-controlled. Therefore, dimer 20 evaporation was likely more pronounced. For this reason, we did not attempt to quantify the dimer evaporation rate, although the dimer signals are quantitatively consistent with the data shown in Fig. 3.
However, the CI-APi-TOFs have a much wider mass range than the CIMS, i.e., a maximum of approximately 2000 Th. This increased mass range allowed larger clusters to be measured; indeed, neutral sulfuric acid clusters containing up to 10 sulfuric acid molecules, i.e., HSO4 -(H2SO4)n (n from 0 25 to 9) were detected (Fig. 8). Eisele and Hanson (2000) previously reported detection of neutral clusters containing up to eight sulfuric acid molecules in a flow-tube experiment using a quadrupole mass spectrometer. However, their measurements were conducted at much higher sulfuric acid concentrations (~10 9 cm -3 ) whereas in this study the conditions were atmospherically more relevant (sulfuric acid monomer concentration ~1.7x10 7 cm -3 ). Therefore, the data presented in the following indicates that atmospheric binary nucleation should be directly observable at low temperature, e.g., during aircraft measurements. Water molecules associated with the clusters were not detected with the CI-APi-TOFs; these were most likely evaporated during ion transfer into the high vacuum section of the instruments.
No ammonia was detected in any of the clusters either, even though ammonia can, in principle, be observed with a similar instrument that measures charged clusters (Kirkby et al., 2011), so it can be The upper panel of Fig. 8 shows the time-resolved signals from one of the CI-APi-TOFs ranging from the monomer (HSO4 -, i.e., S1) up to the decamer (HSO4 -(H2SO4)9, i.e., S10); all of these signals clearly increase following the start of the experiment at 10:02 UTC. From the time-resolved data, the steady-state signals for the different clusters were obtained for both instruments (red and blue symbols in Fig. 8, lower panel). It was not attempted to derive concentrations from the count-rate signals due to 5 the unknown influence of cluster evaporation within the sampling line and transmission within the mass spectrometers. However, the CIMS, which was operated in parallel to the CI-APi-TOFs with its own dedicated sampling line, yielded a monomer concentration of 1.7x10 7 cm -3 .
For this experiment we calculated the extent to which ion-induced clustering (IIC) could contribute to the signals. The equations provided by Chen et al. (2012) were used to estimate the maximum contribution from IIC (Fig. 8,

15
together with the dimer and trimer evaporation rates (from this study and from Hanson and Lovejoy (2006), respectively) allows us to predict all cluster concentrations and then calculate the expected signals (black curve). While the expected signals from the model calculation are substantially higher than the measured ones from the CI-APi-TOF-UFRA, the shape of the black (modeled) and the red (measured) curve is very similar. This suggests that cluster evaporation rates of the trimer and all larger 20 clusters are not high enough to significantly affect their concentrations at this low temperature. The slightly steeper slope of the measurements could be due to a decrease in the detection efficiency as a function of mass of the CI-APi-TOF-UFRA. In this context it is also important to note that the CI-APi-TOF-UFRA was tuned differently than in a previous study  in which a relatively steep drop in the sensitivity as a function of mass was observed. The tuning in this study might have led 25 to a more constant detection efficiency as a function of mass. The fact that the measured trimer signal is lower than the tetramer signal is thought to result from fragmentation of the trimers. Similarly, the hexamer appears to suffer some fragmentation. The CI-APi-TOF-UHEL was tuned to maximize the signals in the mass range up to the pentamer. Consequently, in comparison to the other CI-APi-TOF, this led to substantially higher signals in the mass region up to the pentamer, with a pronounced local 30 maximum around the tetramer (blue curve in Fig. 8). However, for the larger masses the signal drops, reaching levels that are comparable to those from the CI-APi-TOF-UFRA.
Because so many questions remain regarding fragmentation, cluster quantification, and the effect of evaporation in the sampling line, the CI-APi-TOF signals are only discussed qualitatively in the present study.
During CLOUD5, ternary nucleation experiments were conducted at temperatures of 210, 223, and 248 K. The addition of relatively small amounts of ammonia (mixing ratios below ~10 pptv) led to a significant increase in the sulfuric acid dimer concentrations compared to the binary system confirming the enhancing effect of ammonia on new particle formation (Ball et al., 1999;Kirkby et al., 2011;Zollner 5 et al., 2012;Jen et al. 2014). In the presence of NH3, a fraction of the sulfuric acid will be bound to ammonia. However, we assume that the sulfuric acid monomers and dimers will still be ionized by the nitrate primary ions at the same rate as the pure compounds. The ammonia will, however, evaporate very rapidly after the ionization (Hanson and Eisele, 2002). For this reason it is not possible to determine directly the fractions of either the sulfuric acid monomer or the dimer that contain ammonia. Therefore, 10 in the following we assume that the measured monomer is the sum of the pure sulfuric acid monomer and the sulfuric acid monomer bound to ammonia; the same assumption is made for the dimer. It has been suggested that the sensitivity of a nitrate CIMS regarding the sulfuric acid measurements could be affected by the presence of ammonia (or other bases like dimethylamine), which cluster with sulfuric acid Kupiainen-Määttä et al., 2013). However, recent measurements at the CLOUD 15 chamber indicate that this is very likely a minor affect (Rondo et al. 2015). can be seen that, at the lowest temperature (210 K), the dimer concentrations are close to the expected concentrations for kinetically limited cluster formation, as has been previously reported for the ternary sulfuric acid, water and dimethylamine system at 278 K . The ammonia mixing ratio 25 is ~6 pptv in this case (Fig. 9, upper panel). At 223 K two different ammonia mixing ratios were investigated. It can clearly be seen that the dimer concentrations increase with increasing ammonia mixing ratio. Different ammonia mixing ratios (~2.5 to 8 pptv) were also studied at 248 K, but in this case the variation in the ammonia concentration was smaller than for 223 K; therefore, the dimer concentration variation is also less pronounced. In addition, the relative humidity changed from 30 experiment to experiment (RH is indicated by the small numbers written next to the data points); it apparently influenced the dimer concentration, which is not surprising given the results described in Section 3.3, and those of Hanson and Lovejoy (2006). Our data show that very small ammonia mixing ratios (pptv range) can strongly enhance dimer formation under atmospherically relevant sulfuric acid concentrations and low temperatures.
In order to better understand what influences the dimer concentration in the ternary system, we have developed a simple model (Fig. 10). This heuristic model is motivated by recent studies which have simulated acid-base nucleation of sulfuric acid, ammonia, and amines with similar methods, i.e., without simulating every possible cluster configuration explicitly (Chen et al., 2012;Paasonen et al.,  For all larger clusters we make no distinction between pure sulfuric acid clusters and ammonia containing clusters. We further assume that the clusters cannot contain more bases than acids, so reactions like AB + B are not considered as the extra base is expected to evaporate much more rapidly 15 than it can be gained through collisions at the relatively low base concentrations (Schobesberger et al., 2015).
The model differs somewhat from that used by Chen et al. (2012) and Jen et al. (2014). They considered two separate schemes; in their first scheme, they assumed that two different dimer versions exist -a volatile dimer, and a less volatile dimer that is formed through collision between the volatile 20 dimer and a base molecule. The less volatile dimer can form a trimer or a tetramer (through selfcoagulation), which are assumed to be stable. This scheme is similar to pathway (a) described above.
Their second scheme assumes that the sulfuric acid monomer can form a cluster AB, which can be turned into a stable dimer. This dimer can then form a trimer that is allowed to evaporate at a rather slow rate (0.4 s -1 at 300 K). Once the size of the tetramer is reached the cluster is assumed to be stable. Except

25
for the evaporation rate of the base-containing trimer this scheme is identical to route (b) described above. Our approach combines the two channels because it seems likely that dimers can be formed through the two different pathways at the same time (Fig. 10), especially when the temperature is low and the evaporation of A2 is relatively slow. In addition, we assume that the only base-containing cluster that can still evaporate at these low temperatures (248 K and colder) is AB. Quantum chemical 30 calculations (Ortega et al., 2012), and the measurements of Hanson and Eisele (2002) support the assumption that the cluster containing two sulfuric acid molecules and one ammonia molecule is stable even at relatively high temperature (275 K in the Hanson and Eisele (2002) study). Furthermore, since the evaporation rate of the base-containing trimer reported by Chen et al. (2012) is quite small at 300 K (0.4 s -1 ), we assume that, at the very low temperatures of this study, this evaporation rate becomes The quantum chemistry data from Ortega et al. (2012) support the assumption that a trimer containing at least two bases is relatively stable (evaporation rate below 0.1 s -1 at 300 K). However, it predicts that the trimer containing only one ammonia molecule has a high evaporation rate regarding an acid molecule (~1000 s -1 at 300 K); additional ammonia in the trimer will lower the evaporation rates. For this reason the trimer concentration will strongly depend on the ammonia concentration, which controls the cluster 5 distribution. Therefore, the Chen et al. (2012) value can be regarded as a best estimate for the overall trimer evaporation rate for their experimental conditions. Herb et al. (2011) also simulated the effect that one water molecule has on the acid evaporation rate from (H2SO4)3(NH3)1(H2O)0,1 clusters. While the water molecule lowers the evaporation rate the absolute evaporation rate is higher (2.9x10 4 s -1 at 300 K) than for the Ortega et al. (2012) data.

Thermodynamics of the H2SO4•NH3 cluster
Under these assumptions, the model of Fig. 10 was used to probe the kinetics using the measured sulfuric acid monomer, and ammonia concentrations, along with the dimer (A2) and trimer (A3) evaporation rates 15 as a function of relative humidity and temperature from this study and from Hanson and Lovejoy (2006).
The only free parameter in the model is then the evaporation rate of AB; we adjusted this until the modeled dimer concentration matched the measured one under steady-state conditions. From the evaporation rates at the different temperatures the thermodynamics (dH and dS) of the cluster AB were retrieved from a least-square linear fit (logarithm of the equilibrium constant vs. the inverse temperature) 20 which yields dH = -16.1±0.6 kcal mol -1 and dS = -26.4±2.6 cal mol -1 K -1 for H2SO4•NH3.
Unfortunately, the number of data points used to derive the dH and dS values is quite small. At 210 K the measured dimer concentrations are very close to the kinetic limit estimation, so the evaporation rates must be very low. This indicates that small variations in the monomer and dimer concentration can lead to a large variation in the evaporation rate of AB. These data points were, therefore, neglected. On the 25 other hand, the effect of the relative humidity on the evaporation rates of ammonia containing clusters is not known, so only those experiments that were conducted at similar RH, i.e., ~25%, were considered.  we have also simulated the experiments of Hanson and Eisele (2002) for the ternary system involving ammonia, who used a sulfuric acid concentration of 1.9x10 9 cm -3 and an ammonia concentration of 3.8x10 9 cm -3 at a temperature of 265 K and an RH of ~10%. Our calculated dimer concentration agrees with their measured concentration within about 40%. Table 3 shows a comparison with the cluster concentrations (dimer to pentamer) measured by Hanson and Eisele (2002) and the ones from this study using the acid-base model described above.  Ortega et al., 2012;Chon et al., 2014) and from one flow tube experiment (Jen et al., 2014). Overall, the agreement is good. However, it is difficult to take into account the effect the model assumptions have on the outcome of the values from our study. In addition, only a small number of data points have been taken into account in this study.
One also needs to keep in mind that the cluster formation was observed at ~25% RH (with respect to 10 supercooled water) in this study, while most of the theoretical studies did not take into account the effect of water except the one by Nadykto and Yu (2007). Their data suggest that the evaporation rate of H2SO4•NH3•(H2O)x increases when the number of associated water molecules increase. The study by Henschel et al. (2014) indicates that about one water molecule is attached for the RH relevant of this study. However, Henschel et al. (2014) reported their results only for a temperature of 298 K, whereas 15 the temperature of this study is 248 K and lower. Whether the evaporation rate is increasing with increasing RH cannot be concluded from our data, however, one needs to keep in mind that similar to the dimer in the binary system, the reported evaporation rates and thermodynamic data for the H2SO4•NH3 represent average values that can include clusters with attached water molecules.
The comparison in Table 4 also lists the experimental study by Jen et al. (2014) who determined the 20 evaporation rate of H2SO4•NH3 at ~300 K from a transient version of their second scheme (formation of dimers only via AB, see above). The extrapolated value from the present study is, however, in relatively good agreement with their value. The somewhat lower evaporation rate of Jen et al. (2014) could be explained by the fact that they did not consider the formation of dimers by self-coagulation of A. Furthermore, they assumed that the trimer has an evaporation rate of 0.4 s -1 . Both these assumptions 25 require a slower evaporation rate for AB than our study suggests to explain the measured dimer concentrations at a given monomer and base concentration.
Overall, our measurements in the ternary system yield values of the thermodynamic properties of the H2SO4•NH3 cluster that are in rather good agreement with the results from quantum chemical calculations. However, since the number of data points is limited, the uncertainty is rather high.

Uncertainties
The error bars shown in Fig. 4 and 5 include the standard variation of the individual data points and a 30% (50%) systematic uncertainty in the monomer (dimer) concentration. The two error components 35 are added together in quadrature. The systematic errors are estimated based on the uncertainties in the calibration coefficient C for the monomer. Due to the higher uncertainty of the sampling losses for the dimer, and the uncertainty of the transmission correction factor (Section 2.3) a somewhat higher uncertainty has been chosen in comparison to the monomer. The error bars in Fig. 7 are obtained when using Gaussian error propagation on equation (5) for the monomer and the dimer concentration.
In addition to these errors, the effects of evaporation of the dimer in the sampling line (Section 2.6) and fragmentation (Section 3.2) have been discussed above. Each of these effects is very likely on the 5 order of a factor of two or smaller. These processes probably influence all of the dimer data to some extent. However, these errors work in opposite directions: evaporation will lead to a reduction of the dimer concentration, while fragmentation of larger clusters will tend to increase the apparent concentration. Therefore, the two effects partially compensate each other, so they were not taken into account in the calculation of the error bars.

10
One additional uncertainty is introduced by the assumption that the CIMS detection efficiency is independent of temperature. The study of Viggiano et al. (1997) indicates that the collision rate between nitrate primary ions and sulfuric acid is only a weak function of temperature between 200 and 300 K.
Therefore, we expect that temperature only has a small effect on the sulfuric acid concentrations.
The exact values of dimer evaporation rates depend on the choice of G1,1•K1,1, i.e., on the overall 15 collision rate between two neutral dimers and is therefore subject to an additional uncertainty because this value is based on theoretical calculations. However, the thermodynamic data derived in this study does not depend on the value of G1,1•K1,1 because both the data from this study and the one from Hanson and Lovejoy (2006) in Fig. 7 were calculated using the same factors. Therefore, when deriving dH and dS the collision rate cancels out in the calculations (cf. equations (5) and (8)).

20
In contrast to the exact value of G1,1•K1,1 the charged-neutral collision rate k21 between HSO4and H2SO4 is important because its value scales the dimer concentrations and evaporation rates from this study while leaving the data from Hanson and Lovejoy (2006) unaffected. The reported value of 8x10 -10 cm 3 s -1 for k21 from Zhao et al. (2010) suggests that this charged-neutral reaction is not proceeding at the collision limit (value of ~2x10 -9 cm 3 s -1 ). When using the faster reaction rate for the charged-neutral 25 collision limit some of the dimer concentrations would exceed the kinetic limit (cf. Fig. 9, upper panel) because all dimer concentrations would need to be scaled up by a factor of 2.5; therefore the faster rate seems to be implausible. However, using the upper limit for the collision rate results in dH = -23.0±1.6 kcal mol -1 and dS = -58.5±6.9 cal mol -1 K -1 .
The estimates of the thermodynamic properties of the H2SO4•NH3 cluster rely on the assumptions 30 made in the model (Section 3.6). One of the important assumptions made is that the base-containing trimer and tetramer do not evaporate significantly. The data of Ortega et al. (2012) suggest that the evaporation rates of the A3B1 and the A4B1 clusters are not negligible, even at temperatures at and below 248 K. However, the presence of further ammonia molecules in the trimer and tetramer can lower the evaporation rates and water should have a similar effect (Ortega et al., 2012;Herb et al., 2011). In contrast, the base containing dimer (A2B) has a very small evaporation rate. No experimental data have been found that support the relatively high evaporation rates of the base containing trimer and tetramer.
regarding the evaporation rates of these clusters; further experiments will be needed to reduce these in the future.

10
A Chemical Ionization Mass Spectrometer (CIMS) was used to measure the concentrations of the neutral sulfuric acid monomer and dimer during nucleation experiments at the CLOUD chamber. These experiments were conducted at temperatures as low as 208 K, making them relevant to conditions in the free troposphere. Both, the binary (H2SO4-H2O) system, and the ternary system involving ammonia
Comparison of neutral and ion-induced nucleation experiments indicate that the CIMS detected a significant number of fragmented ion clusters. This confirms the so called "ion-effect" on the CIMS measurements that was recently described by Rondo et al. (2014). However, while Rondo et al. (2014) observed that fragmented HSO4 -•OxOrg clusters contributed to the CIMS sulfuric acid monomer 20 measurement, we observed a similar effect for the CIMS sulfuric acid dimer measurement (m/z 195).
Interestingly, the ion effect on the CIMS dimers was almost absent as soon as ammonia was present in the CLOUD chamber. This is consistent with the observation that ammonia stabilizes sulfuric acid clusters and, thereby, enhances nucleation (Kirkby et al., 2011;Schobesberger et al., 2015).
From the measured monomer and dimer signals dimer evaporation rates were derived and compared 25 to previous flow tube measurements made by Hanson and Lovejoy (2006) for the binary system. Their measurements were performed over a temperature range of 232 to 255 K. The data from the present study were obtained at lower temperatures, 208 to 223 K. Together, the two data sets yield a revised version of the Hanson and Lovejoy (2006) formulation for the dimer equilibrium constant at 20% RH with dH = -20.1±1.2 kcal mol -1 and dS = -46.7±5.2 cal mol -1 K -1 . This result is obtained when assuming 30 that the evaporation of larger sulfuric acid clusters (trimer and larger) does not contribute significantly to the dimer concentration, which is the case for the conditions of this study. Due to the wide temperature range (208 to 255 K) covered by the two data sets, this new estimate provides a high degree of confidence when being used at the very low temperatures where binary nucleation can be efficient.
Regarding the formation of dimers in the binary system Hanson and Lovejoy (2006) stated that an 35 increase in the relative humidity leads to an increase in the dimer equilibrium constant (Kp ~ RH p ) with a power dependency of p between 0 and 1. The best estimate for the power dependency was reported to be 0.5 (Hanson and Lovejoy, 2006). Our data indicate that the exponent is around 1 at 208 K and around 1.6 at 223 K, i.e., at the upper end of what has been previously assumed.
The ternary experiments involving ammonia (H2SO4-H2O-NH3) showed that the addition of very small amounts of ammonia (in the pptv range) strongly enhances the sulfuric acid dimer concentration.
The dimer concentrations are systematically higher than those for the binary system at a given 5 temperature and sulfuric acid monomer concentration. Furthermore, they increase with increasing ammonia mixing ratio.

15
Using the proposed model with the evaporation rate of the H2SO4•NH3 cluster as a fitting parameter, the measured dimer concentrations in the ternary system can be reproduced with a high accuracy for the conditions of this study. A previous study suggested that the (H2SO4)2•NH3 cluster is thermodynamically stable (Hanson and Eisele, 2002). With this observation, the model can be used to calculate nucleation rates in the ternary system, which relies on experimentally determined thermo-chemical data and on the 20 assumptions that ammonia containing trimers and tetramers have insignificant evaporation rates for the conditions of this study.
Finally, large neutral sulfuric acid clusters containing as many as 10 sulfuric acid molecules were observed for the binary system at 206 K. These clusters were measured with two Chemical Ionization-Atmospheric Pressure interface-Time Of Flight (CI-APi-TOF) mass spectrometers. Since these 25 measurements were not made with a temperature-controlled sampling line the absolute determination of the cluster concentrations was not attempted. However, the signals are consistent with the assumption that cluster growth is essentially kinetically controlled for all of the observed clusters above the dimer.
The observation of these large clusters at the upper end of atmospherically relevant sulfuric acid monomer concentration of ~1.7x10 7 cm -3 shows that observation of nucleating clusters in the atmosphere should be feasible. In the future, aircraft operation or measurements at high-altitude stations using CI-APi-TOF could provide insight into the importance of binary vs. ternary ammonia nucleation in the free troposphere.   Table 2. Thermodynamic properties (dH and dS) and evaporation rates of the sulfuric acid dimer from this study and from the literature. a Literature data from Ding et al. (2003).

5
'Dimer' is the sum of all clusters containing two sulfuric acid molecules (A2 + A2B + A2B2) and the same applies for the 'trimer' with three sulfuric acid molecules. The arrows indicate the relevant reactions and whether only collisional growth (single-ended arrow) or growth as well as evaporation (double-ended arrow) are important. Losses due to walls, dilution and coagulation are included in the model but not indicated. Small numbers represent concentrations for an example calculation at a