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Journal of Geophysical Research Atmospheres
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Experimental particle formation rates spanning tropospheric sulfuric acid and ammonia abundances, ion production rates and temperatures Andreas Kürten1, Federico Bianchi2,3, Joao Almeida1,4, Oona Kupiainen-Määttä5, Eimear M. Dunne6,a, Jonathan Duplissy4,b, Christina Williamson1, Peter Barmet2, Martin Breitenlechner7,8, Josef Dommen2, Neil M. Donahue9, Richard C. Flagan10, Alessandro Franchin5, Hamish Gordon4, Jani Hakala5, Armin Hansel7,8, Martin Heinritzi1, Luisa Ickes1,c, Tuija Jokinen5, Juha Kangasluoma5, Jaeseok Kim11, Jasper Kirkby1,4, Agnieszka Kupc12, Katrianne Lehtipalo5,d, Markus Leiminger1, Vladimir Makhmutov13, Antti Onnela4, Ismael K. Ortega5,e, Tuukka Petäjä5, Arnaud P. Praplan2,f, Francesco Riccobono2, Matti P. Rissanen5, Linda Rondo1, Ralf Schnitzhofer7,8, Siegfried Schobesberger5,g, James N. Smith11,14, Gerhard Steiner5,6,h, Yuri Stozhkov13, António Tomé15, Jasmin Tröstl2, Georgios Tsagkogeorgas16, Paul E. Wagner12, Daniela Wimmer1,b, Penglin Ye9, Urs Baltensperger2, Ken Carslaw6, Markku Kulmala5, and Joachim Curtius1
1Goethe University of Frankfurt, Institute for Atmospheric and Environmental Sciences, 60438 Frankfurt am Main, Germany. 2Paul Scherrer Institute, Laboratory of Atmospheric Chemistry, 5232 Villigen, Switzerland. 3ETH Zurich, Institute of Atmospheric and Climate Science, 8092 Zurich, Switzerland. 4CERN, Physics Department, 1211 Geneva, Switzerland. 5Department of Physics, University of Helsinki, 00014 Helsinki, Finland. 6University of Leeds, School of Earth and Environment, Leeds LS2 9JT, UK. 7University of Innsbruck, Institute for Ion and Applied Physics, 6020 Innsbruck, Austria. 8Ionicon Analytik GmbH, 6020 Innsbruck, Austria. 9Carnegie Mellon University, Center for Atmospheric Particle Studies, Pittsburgh, PA 15213, USA. 10California Institute of Technology, Division of Chemistry and Chemical Engineering, Pasadena, CA 91125, USA. 11University of Eastern Finland, Department of Applied Physics, 70211 Kuopio, Finland. 12University of Vienna, Faculty of Physics, 1090 Wien, Austria. 13Lebedev Physical Institute, Solar and Cosmic Ray Research Laboratory, 119991 Moscow, Russia. 14National Center for Atmospheric Research, Boulder, CO 80307, USA. 15University of Lisbon and University of Beira Interior, SIM, 1749-016 Lisbon, Portugal. 16Leibniz Institute for Tropospheric Research, 04318 Leipzig, Germany. anow at: Finnish Meteorological Institute, Atmospheric Research Centre of Eastern Finland, 70211 Kuopio, Finland.
1 bnow at: University of Helsinki, Department of Physics, 00014 Helsinki, Finland. cnow at: ETH Zurich, Institute of Atmospheric and Climate Science, 8092 Zurich, Switzerland. dnow at: Paul Scherrer Institute, Laboratory of Atmospheric Chemistry, 5232 Villigen, Switzerland. enow at: Université Lille, Laboratoire de Physique des Lasers, Atomes et Molécules, 59655 Villeneuve d’Ascq, France. fnow at: Finnish Meteorological Institute, 00101 Helsinki, Finland. gnow at: University of Washington, Department of Atmospheric Sciences, Seattle, WA 98195, USA. hnow at: University of Vienna, Faculty of Physics, 1090 Wien, Austria.
Contents of this file
Text S1 to S4 Figures S1 to S8
Introduction
Text S1 describes in detail how the ammonia mixing ratios were derived. The Figures S1 and S2 include information about the gas system used to deliver the ammonia into the CLOUD chamber and its characterization.
Text S2 describes in detail how the nucleation (or new particle formation) rates (J) shown in the main text were derived from the particle measurements. Figure S3 shows a comparison between nucleation rates obtained from different instruments and Figure S4 shows the results of an example calculation.
Text S3 relates to the effect of relative humidity on the particle formation rates under binary conditions at 223 K (Figure S5).
Text S4 explains how the normalization of nucleation rates regarding the sulfuric acid concentration can be performed. This analysis is used to show nucleation rates as a function of the ammonia mixing ratio (see Figures S6 to S8); it yields similar results than the data discussed in Section 3.3 (and Figures 5 to 7) of the main text.
Text S1. Characterization of the ammonia gas system
This section provides a detailed description and characterization of the gas system used for the ammonia delivery into the CLOUD chamber. Since it is not possible to form ammonia in-situ it had to be introduced into the chamber by means of a diluted gas mixture. Although great care has been taken to avoid inhomogeneities and memory effects a careful characterization of the gas system is essential. In the following sections the gas system will be described. The measurement of ammonia with the LOPAP, the IC and the PTR-MS is described elsewhere [Bianchi et al., 2012; Praplan et al., 2012; Norman et al., 2007].
NH3 gas system
The concentration of NH3 inside the CLOUD chamber is controlled by adjusting the flow rates of three different mass flow controllers (MFCs). A schematic drawing of the gas system is shown in
Figure S1. An ultrapure gas mixture of 1% NH3 diluted with nitrogen from a gas bottle 2 (Carbagas) is used to provide the ammonia. The flow rate from the bottle is adjusted with MFC1 and diluted with clean air from the cryogenic N2 and O2 gas supplies controlled by MFC2. To achieve high concentrations of NH3 the gas system allows introducing the diluted flow directly into the CLOUD chamber through a bypass valve. However, for the experiments used here, the bypass valve was closed for most of the time. Instead, another valve (overpressure valve) was used to direct a large fraction of the ammonia containing gas to the exhaust and to use only the small remaining part for the CLOUD chamber by means of MFC3. Downstream to this MFC a constant flow of clean air at 1000 scc/min (scc, standard cubic centimeters) is mixed into the ammonia containing flow in order to achieve a higher flow speed and to minimize memory effects of the pipes. At least 24 hours before an actual ammonia experiment is conducted at CLOUD the flows are enabled as described to condition the pipes, the MFCs and the valves. During this conditioning period the flow is directed to the exhaust through the purge valve. The distance between the chamber valve and the point where the pipe terminates inside the chamber is approximately 23 cm (inner tube diameter is 15 mm). This distance has been minimized to achieve fast conditioning when the NH3 is eventually introduced by opening the chamber valve and closing the purge valve in this defined order. The amount of ammonia introduced into the chamber can be calculated from the fraction of
NH3 inside the gas bottle B (0.01) and the MFC flow rates. When the bypass valve is closed the following amount of ammonia is flown into the chamber:
MFC1 MFC3 A B . (S1) NH3 MFC1 MFC2
The flow rates MFC should be used in cm3 s-1 at standard temperature and pressure (STP), and the quantity ANH3 is the flow rate of NH3. The volume mixing ratio (VMR) of NH3 (in pptv) inside the CLOUD chamber can be calculated from the following differential equation:
dVMRNH3 ANH3 12 10 pptv kw VMRNH3 kdil VMRNH3 CS NH 3 VMRNH3 . (S2) dt Vch
7 3 Here, Vch is the volume of the CLOUD chamber (2.6110 cm ), kw is the wall loss rate constant of ammonia, kdil is the dilution rate constant and CSNH3 is the condensation sink of ammonia on nucleated particles. However, the condensation of ammonia on particle surfaces can be neglected due to the following reasons. The evaporation rate of ammonium-bisulphate clusters is quite high; therefore ammonia can only stick to clusters and particles equal to or larger than the sulfuric acid dimer. Sulfuric acid dimer concentrations are below 4105 cm-3 at maximum for the binary conditions in CLOUD at the lowest temperature [Kürten et al., 2015a]. Using a collision rate of 410-10 cm3 s-1 between the sulfuric acid dimer and ammonia results in an ammonia loss rate of 1.610-4 s-1 due to the dimers which dominate the condensation loss. Furthermore, when ammonia is added to the chamber its concentration is generally much higher than the sulfuric acid concentration. Therefore, if any appreciable depletion of ammonia would occur due to condensation on the growing particles a drop in [H2SO4] would precede because the sulfuric acid concentration is much lower than the concentration of ammonia. Since nucleation rates are only determined over periods of constant sulfuric acid concentration the depletion of ammonia can be ruled out. The dilution rate constant can be calculated from the ratio of the clean gas flow rate that is required to replenish the gas taken by the instruments and the chamber volume. Typically, the flow rate of air into the chamber is 150 liters per minute at STP; therefore the dilution rate constant (assuming homogenous mixing) is 9.610-5 s-1. The wall loss rate is not known a priori but at this point it can be compared to the wall loss rate constant of sulfuric acid which has been
3 experimentally determined as 210-3 s-1. Assuming at this stage that the walls act as a perfect sink the wall loss rate can be assumed to be proportional to the square root of the gas-phase diffusion coefficient [Crump et al., 1982; Metzger et al., 2010] and should be faster for ammonia because its diffusion coefficient is more than a factor of two larger compared to that of sulfuric acid
[Hanson and Eisele, 2000; He et al., 2010]. This means kw is at least 10 times larger than kdil and CSNH3, therefore the dilution and condensation effect can be neglected. Further assuming steady state yields
12 12 12 ANH3 10 pptv ANH3 10 pptv MFC1 MFC3 B 10 pptv F VMRNH3 . Vch kw kdil CS NH 3 Vch kw MFC1 MFC2 Vch kw kw (S3)
The factor F describes the flow of ammonia into the chamber in terms of pptv s -1. The only unknown quantity in this equation is kw, which can be derived from calibration measurements (see further below). During these measurements different flow rates were adjusted and the
VMRNH3 was experimentally determined. It should be noted that kw for ammonia does not describe the wall loss necessarily in the same way as it is the case for sulfuric acid. Sulfuric acid is formed in-situ and therefore homogenously distributed inside the chamber whereas ammonia is introduced through a stainless steel pipe in the vicinity of the lower mixing fan. Regarding the potential loss of ammonia along its inlet lines it should be pointed out that the ammonia mixing ratio is always above several tens of ppbv when it is introduced into the chamber where further dilution leads to the very low mixing ratios. Due to these rather high mixing ratios in the pipes and the long times allowed for equilibration no significant loss is expected. Since turbulence is occurring close to the fan [Voigtländer et al., 2012] and the introduction of ammonia is close to the chamber wall and the fan, it can be expected that the apparent wall loss rate is faster than for sulfuric acid due to a faster deposition of NH3 molecules on these surfaces.
Calibration of the MFCs
The gas system has been characterized by introducing different concentrations of NH3, which were controlled by the MFC flow rates, into the CLOUD chamber. The ammonia mixing ratio was measured either with the IC and, if available, with the PTR-MS. Besides a general characterization of the gas system the MFC calibration is needed (a) to show that the system yields reproducible results throughout the different campaigns and (b) to yield information about the VMRNH3 inside the chamber in case no direct measurement of the ammonia level is available. This was the case during the CLOUD5 campaign when the chamber was mainly operated at
VMRNH3 below 10 pptv and at temperatures below 273.15 K. At these low temperatures the IC does not work because it is limited to temperatures above the freezing point of water. The PTR- MS does not have this limitation with respect to temperature but instead it was suffering from other instrumental problems (like contamination of the sampling line or the zero gas) which made it difficult to yield reliable direct ammonia measurements for most times during CLOUD5. Therefore, a careful evaluation of the relationship between MFC settings and the resulting
VMRNH3 became necessary. Calibration points were recorded during the CLOUD3, CLOUD5, CLOUD6 and CLOUD7 campaigns. Most of these points are shown in Figure S2 (upper panel). Data points obtained from CLOUD3 are shown in Fig. S2 (lower panel) but these were not relevant for the conditions of this study (see discussion below). Out of the ten points shown (Figure S2, upper panel) eight were recorded by the IC at 278 K. The PTR-MS contributed one point at 278 K and another one at 223 K. A linear fit through all the data points weighted with respect to the error bars yields a slope of 100.3 s. The error bars include the standard deviation of the measured data points for one flow
4 rate setting plus a systematic error of 20%. The intercept for an ammonia flow rate of zero, i.e., when the chamber valve was closed, is constrained to 2 pptv (-50/+100% error based on the uncertainty of the IC measurement and the variability of the background mixing ratio) at 278 K. This mixing ratio is based on the measurement of the IC when no ammonia was added to the chamber. The background value is, however, close to the detection limit of the IC, which is between 0.2 and 3.7 pptv [Praplan et al., 2012]. It has to be noted also that the background ammonia level is assumed to be strongly temperature dependent, which follows from the APi- TOF data (the section “Ammonia in charged clusters measured by the APi-TOF mass spectrometer” in the SI). The ammonia background at 223 K is negligible compared to the background at 278 K, which has been evaluated as 2 pptv (see above). Therefore, a value of 2 pptv has been added to the PTR-MS data point at 223 K in Figure S2 (upper panel) such that all data points refer to 278 K.
The measured ammonia mixing ratios depend linearly on the amount of NH3 introduced into the chamber. It is also worth mentioning that the calibrations performed during three different campaigns yield almost identical results. Furthermore, the NH3 concentration inside the chamber which comes from the gas system seems to be independent of the chamber temperature. This is supported by the PTR-MS measurement at 223 K which is consistent with the IC measurements performed at 278 K for the same MFC settings. The fitted slope of 100.3 s indicates that the -3 -1 effective wall loss rate of the introduced NH3 is 9.9710 s and therefore about 5 times higher compared to the one of sulfuric acid. The rather short NH3 life-time is partly due to the faster diffusion of ammonia but very likely also due to a high loss rate onto the chamber and fan surfaces which are close to the stainless steel pipe which is used to transport the ammonia into the chamber.
For the CLOUD3 experiment the NH3 mixing levels could not be determined solely from the MFC settings since the concentrations were much higher compared to CLOUD5 and CLOUD7, reaching values up to 1400 pptv maintained over several days. A comparison between the calibration curve from Figure S2 (upper panel) with the data from CLOUD3 (Figure S2, lower panel) shows that the effective wall loss rate is about a factor ~7 lower during CLOUD3. Therefore, there must have been a substantial wall saturation effect during CLOUD3 due to the high concentrations. The LOPAP and the PTR-MS measurements were therefore used to determine the NH3 mixing ratios in CLOUD3. Only during the periods when the very high mixing ratios were applied in CLOUD3 the wall loss is expected to depend on the previous exposure. For the other cases when low ammonia mixing ratios were established this effect was not significant.
Background ammonia levels at low temperatures
Determination of the background ammonia is challenging because the detection limit of the IC is close to 2 pptv at 278 K [Praplan et al., 2012]. This is substantially better than the detection limit of ~35 pptv for the LOPAP, which was used during the CLOUD3 campaign [Kirkby et al., 2011; Bianchi et al., 2012]. Kirkby et al. [2011] hypothesized that the ammonia background originates from the water supply, which has been suggested also by Ball et al. [1999]. However, in the meantime the ammonia content of the water supply in CLOUD has been directly measured by the
IC. This measurement showed that it is very unlikely that the background NH 3 is coming from the water supply. The concentration of ammonia in the water which would be necessary to explain 2 pptv inside the chamber would be well above the detection limit of the IC. Another more likely source of the background ammonia is desorption from surfaces [Vaittinen et al., 2014]. This assumption is supported by the fact that the ammonia background contamination seems to be a strong function of the temperature [Kirkby et al., 2011], i.e., with decreasing temperature the ammonia background becomes substantially lower [Schobesberger et al., 2015]. Therefore, we
5 applied the following method to estimate the background ammonia mixing ratio as a function of the chamber temperature:
E exp a R T T VMR T 2pptv . (S4) NH3,bg E 278K exp a R 278K
Here, Ea is the activation energy of a desorbing NH3 molecule from the stainless steel surface, R (8.314 J K-1 mol-1) is the universal gas constant and T is the temperature. Equation (S4) scales the 7 -3 constrained background NH3 of 2 pptv (i.e., ~510 molecule cm ) at 278 K to other temperatures. The factor T/278 K takes into account that the density of the chamber gas increases with decreasing temperature. To our knowledge no published data exists which describes the surface desorption of NH3 from an electropolished stainless steel surface. Therefore, an activation energy of Ea = 33 kJ/mol is tentatively used, which has been derived as a best estimate for a desorbing water molecule from a stainless steel surface [Tóth, 1999]. It is expected that both water as well as ammonia form hydrogen bounds on the surface and therefore behave in a similar way. Using the value of the activation energy in equation (S4) the ammonia background can be calculated. The results indicate an ammonia mixing ratio of ~2.5105 molecule cm-3 due to desorption at the lowest temperature of 208 K. If desorption is indeed the source of our contaminant NH3 then it would result in a rather constant source of ammonia over a long time since these low levels in the pptv range and below could be maintained over a long time even if just a tiny fraction of the chamber surface were covered with ammonia.
Even though it is attempted to quantify the NH3 level for the nominally binary runs by this method, we are aware that the derived values are quite uncertain (error discussion given in the next section). Nevertheless, it is a reasonable assumption that the background ammonia is not zero even at the lowest chamber temperature and the above described method is one possibility to assign an ammonia mixing ratio to every nucleation experiment. Whether the background ammonia is efficiently contributing during ion-induced nucleation can be determined from the APi-TOF mass spectra [Schobesberger et al., 2015].
Overall NH3 mixing ratio and differences to Kirkby et al. [2011]
If no direct measurement is available the ammonia mixing ratio is calculated according to
F VMRNH3,total T VMRNH3,bg T . (S5) kw
-3 -1 The wall loss rate constant kw has a value of 9.9710 s (see section “Calibration of the MFCs”), the factor F is determined from the MFC settings (equation (S3)) and the background ammonia mixing ratio VMRNH3,bg is a function of the chamber temperature T. This background level is 2 pptv at a temperature of 278 K and calculated according to equation (S4) for other temperatures.
The error on VMRNH3,total includes a 50% uncertainty on the ammonia life-time as well as a -50/+100% uncertainty of the background ammonia at 278 K. The uncertainty of the temperature dependency of the background ammonia level is taken into account by varying the activation energy in equation (S4) to 25 kJ/mol and 40 kJ/mol to yield an upper and lower background concentration, respectively. The ammonia mixing ratios were calculated according to equation (S5) for the low temperature experiments (< 278 K) during CLOUD5 and CLOUD7. For
6 CLOUD3 the ammonia levels were determined from the LOPAP measurement when the MFCs were used to actively introduce ammonia into the chamber. When the ammonia was only present at background levels its concentration follows equation (S5) as a function of temperature.
The study by Kirkby et al. [2011] already presented some of the ternary NH 3 CLOUD3 data for temperatures of 278 and 292 K. In their study the upper limit of the ammonia background was stated as 35 pptv, which is the detection limit of the LOPAP instrument. However, we think that already in CLOUD3 the background ammonia was lower and therefore are using the same background levels at the respective temperature for all campaigns. The 2 pptv at 278 K were measured during CLOUD5 with the IC instrument [Praplan et al., 2012].
Ammonia in charged clusters measured by the APi-TOF mass spectrometer
The APi-TOF (Atmospheric Pressure interface-Time Of Flight) mass spectrometer is capable of detecting the presence of ammonia in charged sulfuric acid clusters during nucleation [Kirkby et al., 2011]. Kirkby et al. [2011] reported the presence of ammonia molecules in the tetramer – ((H2SO4)3•HSO4 ) and in larger clusters. However, ammonia rapidly evaporates from the charged – – – monomer (HSO4 ), the dimer (H2SO4•HSO4 ) and also from the trimer ((H2SO4)2•HSO4 ) and does therefore not stabilize the smallest charged clusters [Schobesberger et al., 2015]. In the neutral channel this is different because ammonia has already a stabilizing effect on the dimers [Hanson and Eisele, 2002; Ortega et al., 2012; Kürten et al., 2015a]. Nevertheless, the APi-TOF spectra can be used to qualitatively determine the presence or absence of ammonia in the charged clusters. In the beginning of charged nucleation ammonia will not efficiently participate in the – nucleation because it will quickly evaporate from all charged clusters (H2SO4)n•HSO4 with n < 3. If ammonia is even absent from the larger clusters n 3 it means that the ammonia level is low enough such that pure binary nucleation is proceeding. If ammonia is present in the charged nucleation channel it is an indication that it will also assist in the neutral nucleation and very likely will have an even larger effect there because its stabilizing effect begins already with the formation of neutral dimers. On the other hand, even very small contaminant ammonia levels will show up in the APi-TOF signals because charged sulfuric acid clusters will collect ammonia molecules and form stable clusters. The presence of these mixed clusters can then be used to detect ammonia. Schobesberger et al. [2015] defined a parameter which indicates the efficiency at which ammonia participates in the growth of charged clusters. This parameter relates to the signals – measured for the clusters (NH3)m•(H2SO4)n•HSO4 , where the index m represents the number of ammonia molecules and the index n the number of sulfuric acid molecules in the cluster. The composition of clusters was characterized by the number of ammonia molecules m added for each added H2SO4 molecule n, i.e. by the ratio Δm/Δn. For negatively charged clusters the ratio was calculated as the average for 4 ≤ n ≤ 18. It was found that Δm/Δn saturates between 1 and 1.4 for
[NH3]/[H2SO4] > 10 and approaches 0 when the ratio level is smaller than 0.1. The transition occurs when the concentrations of ammonia and sulfuric acid are approximately the same, i.e., when [NH3]/[H2SO4] 1. However, a slight temperature dependency was found also, which can be explained by the fact that the vapor pressure of ammonia varies less steeply with temperature than the vapor pressure of sulfuric acid. More information on the APi-TOF and what information regarding sulfuric acid ammonia clusters can be obtained from its data is found in Schobesberger et al. [2015] and also in Duplissy et al. [2015].
Text S2. Determination of the nucleation rate J1.7
We derive J1.7 from particle number density measurements in a two-step process. First, we determine J3.2 (the particle formation rate at 3.2 nm). This is based on a number balance between 7 N3.2, i.e. the total particle number ≥ 3.2 nm measured with an ultrafine Condensation Particle Counter (CPC) 3776 (TSI, Inc.), which has a 50% detection cutoff at 3.2 nm and the particle losses above that cutoff size [Kürten et al., 2015b]:
n n n dN3.2 J 3.2 Ni kw d p,i N3.2 kdil i, j kcoag d p,i ,d p, j Ni N j . (S6) dt i0 i0 ji
The scanning mobility particle sizer (SMPS) is used to take into account the size distribution (indices i and j from 1 to n) of particles larger than ~3.8 nm. The particle concentration in the zeroeth size bin (index i and j = 0) is obtained from the total particle concentrations measured by the SMPS and the CPC:
n N0 N3.2 Ni . (S7) i1
The diameter corresponding to this bin is taken as the geometric diameter of the two cut-off 0.5 diameters for the CPC and the SMPS, i.e. dp,0 = (3.2 nm 3.8 nm) = 3.49 nm. In most cases the dominant particle losses are to the chamber walls. The size-dependent wall loss rate kw is calculated according to [Crump et al., 1982]
k w d p,i C Dd p,i , (S8) where C (0.0077 cm-1 s-0.5) is a constant determined from the measured decay times of sulfuric acid and particles inside the CLOUD chamber and D (in cm2 s-1) is the particle diffusivity -5 -1 calculated as function of particle diameter dp. The dilution rate constant kdil (9.610 s ) is independent of particle size and follows from the ratio of the flow rate of the replenished gas and the chamber volume. In some cases coagulation (coagulation rate kcoag) also contributes to the particle losses. All possible collisions between particles in different size bins are taken into account by the last term in equation (S6). In this term the factor δi,j (δi,j = 0.5 when i = j and δi,j = 1 otherwise) avoids counting collisions between identical bins twice [Seinfeld and Pandis, 2006; Kürten et al., 2015b].
In a second step J1.7 is calculated from J3.2. Traditionally, an equation (widely known as the Kerminen and Kulmala equation) is used, which adjusts the particle formation rate determined at a larger size to a smaller diameter [Weber et al., 1997; Kerminen and Kulmala, 2002]. However, this equation was derived for ambient nucleation events and can introduce inaccuracies when applied to chamber experiments [Kürten et al., 2015b]. Therefore, an alternate method is used. When the particles grow from 1.7 nm to 3.2 nm they are subject to the same loss processes as the larger particles (see above). Therefore, the formation rate at 1.7 nm will always be larger than the one at 3.2 nm. The correction that needs to be applied to yield J1.7 depends on the loss rates (high loss rates will make the correction larger) and on the particle growth rate GR (high growth rates tend to decrease the correction because the particles have less time to suffer from losses). Growth rates between 1.7 and 3.2 nm are derived from the relative appearance times in the different size channels of the Neutral Air Ion Spectrometer (NAIS), the Di-Ethylene-Glycol- CPCs (DEG-CPCs), the ultrafine CPC 3776 (TSI, Inc.) and the Particle Size Magnifiers (PSMs) [Lehtipalo et al., 2014].
The corrected J1.7 was approximated by the following equation:
8 3.2nm 1.7nm J1.7 J 3.2 1 LR , (S9) GR where the last term ((3.2nm–1.7nm)/GR) represents the time required for the particles to grow from 1.7 nm to 3.2 nm; the factor LR represents the three different loss rates according to:
1 N N LR kw d p,x kdil i, j kcoag d p,i ,d p, j Ni N j , (S10) N3.2 i0 j i
where dp,x is taken as the geometric mean between the two particle diameters 1.7 and 3.2 nm (i.e., dp,x = 2.33 nm). Equation (S9) makes several simplifying assumptions: (1) the correction factor is small and can be approximated by a linear term (1+x, instead of an exponential term exp(x)), (2) overall the three loss processes are size-independent, and (3) the effect of self-coagulation (i.e., the loss of particles due to coagulation among particles with sizes smaller than 3.2 nm) is negligible. Since the correction factors are usually rather small assumption (1) is fulfilled for most experiments. Assumption (2) is strictly not valid as the losses are dominated by wall loss, which decreases with
1/dp. However, the error due to this approximation is small. Comparison with an exact formula from Kürten et al. [2015b] taking into account the actual size-dependence of the wall loss rate shows that the error is negligible when using the geometric mean diameter (2.33 nm) mentioned above. Assumption (3) is mostly fulfilled except for very strong nucleation. However, in the case of the chemical systems investigated in this study this effect is considered to be low. For this reason in CLOUD, traditionally, the linear approximation was used and is therefore also used here. The error on the nucleation rates contains its statistical variation, and additionally, a ±50% uncertainty regarding the correction factor used to transfer the formation rate J3.2 to J1.7, which relates to the uncertainty in GR. The third factor contributing to the overall error includes a ±30% systematic uncertainty on J1.7. This error is estimated from the reproducibility under nominally identical conditions. The three error components are added in quadrature to yield the total error. In addition, we conclude from the intercomparison with formation rates derived from measurements with other condensation particle counters (see below) that there is an uncertainty of a factor 2, most likely due to the approximations mentioned above. As this is rather constant between data points it is not indicated in the plots showing the nucleation rates.
Two methods were applied to verify the accuracy of the applied equations for the J1.7 evaluation. In addition to the procedure described in this section, a recently developed iterative method for calculating nucleation rates was tested [Kürten et al. 2015b]. The method by Kürten et al. [2015b] takes into account the effect of self-coagulation within the size-range between 1.7 and 3.2 nm, which could be important in some cases. In addition, the correct size-dependencies for the loss processes are implemented in the method. Most experiments analyzed by these two different methods agree within a factor of two or better. This indicates that there is no systematic difference between the methods for the reported conditions. The iterative method can sometimes strongly amplify errors in the growth rate and generally requires experiments where conditions are maintained close to steady-state over a longer time. Due to these reasons and because the results of the two methods agree quite well, when a comparison was possible, it was decided to use the previously used method explained above. A second comparison involves formation rates derived from measurements with Condensation Particle Counters (CPCs), which have a lower cut-off size close to a mobility diameter of 1.7 nm. Since these CPCs were not available continuously throughout the campaign in contrast to the ultrafine CPC 3776 (TSI, Inc.) a comparison can only be performed for a subset of nucleation
9 experiments which are reported in a companion paper by Duplissy et al. [2015]. Figure S3 shows the comparison for two different counters (DEGa and PSMb) with the nucleation rates from this study. The generally good agreement leads us to the assumption that the applied methodology is suitable and does not introduce significant systematic uncertainties. However, it should be noted that especially for the formation rates larger than about 1 cm-3 s-1 there exists the possibility of a small bias between the two data sets meaning that the rates from this study are somewhat larger than the ones from Duplissy et al. [2015]. This can possibly be explained by the fact that the particle size for which Duplissy et al. [2015] evaluated their rates is somewhat larger than the 1.7 nm used in this study.
Particle formation rate evaluation example
Figure S4 shows an example for a neutral nucleation run. The formation of sulfuric acid is initiated by turning on the UV light in the chamber. A constant [H 2SO4] is reached when the production rate (due to the oxidation of SO2 with OH) and the loss rate (mainly wall loss) are about the same. At around 18:06 UTC the CPC 3776 starts detecting newly formed particles.
From this data and the SMPS size distribution (not shown) the particle formation rate J3.2 can be calculated (grey curve). Two components for calculating J3.2 are shown in addition: (1) the time derivative of the particle concentration and (2) the overall loss rates corresponding to the last three terms in equation (S6). Applying the methods described in the previous section the formation rate J1.7 can be obtained (green curve). In this example a growth rate of 7.5 nm/hr was used; the factor LR corresponds to 8.210-4 s-1. Averaging the data over a period of constant conditions yields the final value of the particle formation rate at 1.7 nm.
Text S3. Effect of RH at 223 K.
Although no systematic variation of the relative humidity (RH) was performed, the RH was varied during the nominally binary runs at 223 K. At these conditions different RHs were investigated (11%, 25% and 50%; see Figure S5). The RH effect is further discussed by Duplissy et al. [2015].
Text S4. Normalized formation rates as function of ammonia mixing ratio
Section 3.3 of the main text describes the dependence of the nucleation rates on the ammonia mixing ratio. Data regarding this dependence is shown by plotting the nucleation rates for different ammonia mixing ratios over a narrow range of sulfuric concentrations (Figure 5 to Figure 7). In addition, Figures S6 to S8 show the nucleation rates against the ammonia mixing ratio for all sulfuric acid concentrations. This requires normalizing J with respect to [H2SO4] according to one of the following equations:
b H SO 2 4 norm , (S11) J1.7,norm H2SO4 J1.7 H2SO4 . (S12)
The errors in the normalized nucleation rates were calculated with similar formulas. The concentration [H2SO4]norm is chosen according to the midpoint sulfuric acid concentrations
10 provided in Section 3.3 of the main text. Furthermore, the parameters from Table 2 (main text) are used for the normalization. In general, the normalized nucleation rates show very similar trends as the directly measured ones. Therefore, for a general discussion the reader is referred to the main text (Section 3.3). One main difference exists at a temperature of 248 K for ammonia mixing ratios between ~1 and 10 pptv. The directly measured formation rates (Figure 6, upper panel) appear to show enhanced values for the gcr in comparison to the neutral conditions, while the charge effect is insignificant when showing the normalized formation rates including more data points (Figure S7, upper panel). For this reason it seems likely that the charge enhancement is suppressed when ammonia is present in the low pptv-range at 248 K.
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14 Figure S1. Schematic drawing of the gas system providing NH3 to the CLOUD chamber.
15 Figure S2. Upper panel: Calibration curve derived from measurements with the IC and the PTR- MS during the CLOUD5, CLOUD6 and CLOUD7 campaigns. Note that the offset at zero flow of ammonia has been constrained to 2 pptv. Lower panel: Calibration points obtained from CLOUD3 when much higher ammonia mixing ratios were established in the chamber. See text for details.
16 Figure S3. Comparison between particle formation rates from this study and rates derived from measurements with a Di-Ethylene Glycol-CPC (DEGa with a 50% detection efficiency of ~2 nm) and a Particle Size Magnifier (PSMb with a 50% detection efficiency between 1.6 and 1.8 nm) [Duplissy et al., 2015]. Note that only a subset of the formation rates from this study is shown since the DEGa and the PSMb were not available during all experimental runs. The dashed-dotted lines indicate a range of a factor 2 around the 1:1 line.
17 Figure S4. Example of a neutral nucleation run at 278 K. The formation of sulfuric acid (red line) is initiated by adjusting the UV light intensity. The particle concentration larger than about 3.2 nm (blue curve) starts to increase around 18:06 UTC. Particle formation rates are derived for 3.2 nm (J3.2, grey curve) and 1.7 nm (J1.7, green curve). The calculation of the formation rates requires taking into account the time derivative of the particle number concentration (shown for particles larger than 3.2 nm by the dashed grey curve) and the overall loss rate (shown for particles larger than 3.2 nm by the dotted grey curve). The black horizontal arrow marks the time period over -3 -1 -3 -1 which the nucleation rates are averaged (J1.7 = 9.8 cm s , J3.2 = 6.1 cm s ).
18 Figure S5. Particle formation rates as a function of the sulfuric acid concentration at 223 K in the binary system. The data is the same as in Fig. 1 (lower panel) of the main text except that the color code indicates the relative humidity over supercooled water. The adjusted RH was 11, 25 and 50%, respectively.
19 Figure S6. Nucleation rates as function of the ammonia mixing ratio. The nucleation rates are 6 -3 normalized with respect to [H2SO4]. The [H2SO4] for the normalization is 1.710 cm for 208 K (upper panel) and 6.2106 cm-3 for 223 K (lower panel). The functional relationships used for the normalization can be found in Table 2 (main text). The colored lines represent the nucleation rates calculated by ACDC for neutral, gcr and pion beam conditions.
20 Figure S7. Nucleation rates as function of the ammonia mixing ratio. The nucleation rates are 7 -3 normalized with respect to [H2SO4]. The [H2SO4] for the normalization is 110 cm for 248 K (upper panel) and 6.5107 cm-3 for 278 K (lower panel). The functional relationships used for the normalization can be found in Table 2 (main text). The colored lines represent the nucleation rates calculated by ACDC for neutral, gcr and pion beam conditions.
21 Figure S8. Nucleation rates as function of the ammonia mixing ratio for a temperature of 292 K.
The nucleation rates are normalized with respect to [H2SO4]. The [H2SO4] for the normalization is 1.5108 cm-3. The functional relationships used for the normalization can be found in Table 2 (main text). The colored lines show the calculated nucleation rates by ACDC for neutral, gcr and pion beam conditions.
22