Ion – particle interactions during particle formation and growth at a coniferous forest site in central Europe

Introduction Conclusions References

a rapid decrease of the time difference between the ion and total modes during the growth 23 process. Eventually, this time delay vanished when both ions and total particles did grow to 24 larger diameters. Considering the growth rates of ions and total particles separately, total 25 particles exhibited enhanced growth rates at diameters below 15 nm. This observation cannot 26 be explained by condensation or coagulation, because these processes would act more 27 efficiently on charged particles compared to neutral particles. To explain our observations, we 28 propose a mechanism including recombination and attachment of continuously present cluster 1 ions with the ion nucleation mode and the neutral nucleation mode, respectively. 2 3 1 Introduction 4 Tropospheric new particle formation (NPF) is a worldwide phenomenon (Kulmala et al., 5 2004a; Kulmala and Kerminen, 2008) contributing to the global particle number and total 6 amount of cloud condensation nuclei (Makkonen et al., 2012, Merikanto et al., 20097 Spracklen et al., 2006;). The first step leading to NPF is thought to be the formation of stable 8 clusters from precursor gas phase components as sulfuric acid, amines, ammonia and organic 9 vapors (Almeida et al. 2013;Kulmala et al., 2013;Schobesberger et al., 2013). The formation 10 of stable clusters happens in the mobility diameter (D m ) range between 1 to 2 nm. Once 11 formed, the stable clusters are activated and experience rapid growth (Kulmala et al., 2013). 12 Atmospheric ions are very likely to play a considerable role in atmospheric nucleation 13 processes, as ions reduce the critical cluster size and facilitate cluster activation (e.g. Enghoff 14 and Svensmark, 2008;Winkler et al., 2008;Yue and Chan, 1979). In fact, comprehensive 15 field measurements of NPF events at different locations in Europe showed an earlier 16 formation of charged particles compared to total particles (neutral + charged particles; 17 Manninen et al., 2010). Furthermore, the charging state of aerosol particles during NPF was 18 observed to be frequently overcharged (Gagné et al., 2010;Iida et al., 2006;Laakso et al., 19 2007). The ratio of charged particle concentrations to neutral particle concentrations in a 20 defined diameter interval is defined as the charged fraction. In a bipolar ion environment, the 21 size-dependent charged fraction of an aerosol will eventually reach an equilibrium charging 22 state due to ion-particle interactions (Fuchs, 1963;Wiedensohler, 1988). When the charged 23 fraction is elevated in comparison to the equilibrium charged fraction, an aerosol is defined to 24 be in an overcharged charging state. 25 When ions are involved in the nucleation process, two terms are usually used: ion induced 26 nucleation (IIN: e.g. Manninen et al. (2010)) and ion mediated nucleation (IMN; e.g. Yu and 27 Turco (2000)). IIN denotes the formation of particles from small ionic clusters, preserving the 28 charge during growth process. Additionally, when interactions of ions and particles are taken 29 into account the term IMN is used. Hence, IMN includes IIN and does also consider 30 interactions among ions and particles, like recombination and attachment. 31 generates intermediate ions due to the balloelectric effect (Tammet et al., 2009). 23 Only during the last decade, appropriate instrumentation became available to measure neutral 24 and charged cluster size distributions down to diameters relevant for NPF (Kulmala et al., 25 2012). One instrument capable of measuring ions down to D m of about 0.8 nm and neutral 26 particles down to 2 nm is the neutral cluster and air ion spectrometer (NAIS) (Manninen et al., 27 2009b;Mirme and Mirme, 2013). In this paper, we present measurements performed 28 with the NAIS during NPF. A new approach to evaluate the data is proposed to elucidate the 29 interactions of ions and neutral particles in the formation and growth of atmospheric particles. 30 31 the particle mode set to 66 seconds, the ion mode set to 67 seconds and the offset mode set to 23 67 seconds. Therefore, the overall temporal resolution of the NAIS was 200 seconds. 24 In particle mode, the recorded number size distribution is inverted by the instrument software, 25 assuming the Fuchs-charge equilibrium of the sample prior to charging and that all classified 26 particles are singly charged. However, if the particle population is not in charge equilibrium 27 but either overcharged or undercharged, the NAIS will overestimate or underestimate the total 28 particle concentrations, respectively (Kulmala et al., 2012). Additionally, an overestimation of 29 the total particle concentration by a factor of 2-3 is a general characteristic of NAIS 30 instruments, as was shown by an intercomparison of several NAIS instruments by Gagné et 31 merged with this data by means of a linearly weighted merging algorithm in the overlapping 23 region of both instruments between 15 and 27 nm. The mobility particle size spectrometer 24 was measuring with a 5 minute temporal resolution and its size bins were different from the 25 NAIS size bins. Both the size bins and the time resolution were interpolated to match the 26 NAIS time resolution and size bins. The resultant particle number size distribution between 27 2 nm and 680 nm was used for calculating the sink rates for ions and total particles according 28 to Hõrrak et al. (2008), Kulmala et al. (2012) and Tammet and Kulmala (2005). 29 30 2.2 Interactions of ions and neutral particles 1 The major interactions of ions and neutral particles among themselves and with the 2 background aerosol particle population are (1) coagulation of neutral particles, (2) attachment 3 of ions to neutral particles and (3) recombination of ions with ions of opposing polarity. The 4 magnitude of these interactions can be calculated theoretically as corresponding coefficients 5 (see appendix for the formulations). 6 Coagulation (1) is an important sink for freshly nucleated particles and a factor enhancing the 7 particle growth rate (GR) during NPF events (Kulmala et al., 2004b). To determine the size-8 dependent coagulation coefficient ‫ܭ‬ , an approximation from Tammet and Kulmala (2005)  9 was used (cf. Eqs. A1 and A2). The theoretical approach for ‫ܭ‬ is valid for the interaction of 10 neutral particles and clusters of all diameters i and j. 11 The ion aerosol attachment (2) is described by the attachment coefficient ߚ for the interaction 12 of small air ions with neutral particles. ߚ is commonly assumed constant (1x10 -8 cm³ s -1 ) when 13 determining ion formation rates, where the attachment of small ions to neutral particles of a 14 large diameter is considered a source for ions of the same diameter (Hirsikko et al., 2011;15 Kulmala et al., 2012;Manninen et al., 2010). However, this size-independent approach is only 16 an approximation. In particular, when the diameter i of neutral particles is greater than 10 nm, 17 a constant value is inaccurate (cf. green solid line in Fig. 1). Therefore, when calculating ion 18 sinks, the size dependence of ߚ has to be taken into account. The size dependent ߚ varies by 19 three orders of magnitude, when the interactions of small ions of size j with neutral particles 20 of size i are considered (cf. solid green line in Fig. 1 ;Hoppel and Frick, 1990;Hõrrak et al., 21 2008;Tammet and Kulmala, 2005). For this study, we determined ߚ by applying a 22 formulation by Hõrrak et al. (2008), which is an approximation of the tabulated results by 23 Hoppel and Frick (1990) (cf. Eqs. A3 and A4). Since intermediate and large ions also have a 24 slightly enhanced attachment probability compared to pure neutral coagulation (cf. Fig. 1, 25 dashed lines), we extrapolated ߚ for all measured ion size ranges, still using the formulation 26 by Hõrrak et al. (2008). 27 In principle, the ion-ion recombination (3) can also be described by the attachment 28 coefficient, assuming the interaction of clusters with opposite charges. Usually, the 29 recombination coefficient is denoted as ߙ and assumed to be constant (1.6x10 -6 cm³ s -1 ) when 30 the interaction among small ions is considered (Hoppel and Frick, 1990;Kulmala et al., 2013;31 Tammet and Kulmala, 2005). Considering the case of cluster ions of diameter j interacting 1 with oppositely charged clusters of a similar diameter k, ߚ should be comparable to the 2 constant value of α (Hoppel and Frick, 1986). In fact, ߚ for ions with j = 1.5 nm interacting 3 with oppositely charged ions with k = 1.5 nm, as used in this study, is 1.3x10 -6 cm³ s -1 (solid 4 orange line in Fig. 1). Therefore, ߚ for the interaction of oppositely charged clusters in the 5 sizes class j and k, i.e. the size-dependent recombination coefficient, will be denoted as ߙ in 6 the following (Eq. A5). 7 The theory for ion attachment and recombination was developed to calculate the attachment 8 of small ions to larger particles or ions, in order to theoretically assess the particle charge 9 distribution in a bipolar ion environment (Hoppel and Frick, 1986;1990;Reischl et al., 1996). 10 The interaction of intermediate and large ions with even larger neutral or charged particles 11 was not the aim of these studies. Nevertheless, the sinks and sources for all ion sizes have to 12 be taken into account when analyzing ion interactions in NPF. Therefore, we chose to use the 13 approximated theory from Hõrrak et al. (2008) to obtain a first order approximation of the 14 coefficients governing the behavior of larger ions, and to apply the calculations also for larger 15 diameters. A validation of this approach is given by comparing the size dependence of β and α 16 to K. In Fig. 1, all three coefficients are depicted for aerosols of two different diameters (1.5 17 and 10 nm). As electrical effects will enhance the probability of an encounter of two particles, 18 K is the lower limit for the three considered interactions. When small ions (1.5 nm) and small 19 neutral particles interact with each other (green solid line in Fig. 1), the electrical effect can 20 enhance the collision probability by more than one order of magnitude. Considering the 21 interaction of oppositely charged ions, the enhancement can be greater than three orders of 22 magnitude (orange solid line in Fig. 1). The largest differences are found for interactions of 23 small particles or ions. However, when small ions interact with larger particles or ions, α and 24 β approach K, indicating a smaller influence of the charge on the collision probability. A 25 similar pattern can be seen when considering the interaction of large ions with larger aerosol 26 particles (dashed lines in Fig. 1). For the interaction of particles or ions with a diameter of 27 10 nm, α and β decrease about 1-2 orders of magnitude while K is not that strongly affected. 28 The difference among the three coefficients is less pronounced, pointing towards a smaller 29 influence of the charge on collision probabilities when larger ions and particles are 30 considered. 31

Ion-ion recombination 1
Knowing the recombination coefficient ߙ and the number concentration of ions of both 2 polarities, a theoretical number size distribution of neutral particles from ion-ion 3 recombination can be deduced. Kontkanen et al. (2013) and Kulmala et al. (2013) proposed a 4 method to calculate the number size distribution resulting from recombination. Both authors 5 used a constant value of 1.6x10 -6 cm³ s -1 for α. This is justified since only recombination of 6 charged clusters below 2.1 nm in diameter was considered. However, we use the size-7 dependent ߙ for our approach as the recombination of charged clusters up to 42 nm is 8 considered. Furthermore, Kulmala et al. (2013) where, ܰ is the number concentration of recombined neutral particles in size class i and 23 ‫ݎ‬ is a coefficient allocating the recombined neutral particles to size class i. proposed by Kontkanen et al. (2013) and Kulmala et al. (2013) is not taken into account in 28 our formulation. Since the concentration of recombination products did never reach the 29 measured neutral cluster concentration, making the determination of a breakup term 1 impossible. 2 The key parameter governing the concentration of small ions in the atmosphere is the 3 ionization rate Q. For our site, Q was calculated by means of a simplified ion equilibrium 4 equation, assuming steady-state equilibrium (Hoppel and Frick, 1986). This equation assumes 5 the ion production rate to be a function of two ion sink terms, the recombination and the 6 attachment of ions to the present background aerosol (cf. Eq. A8). 7 8

Formation-and growth rate 9
The formation rate J describes the flux of particles or ions into a defined size interval. J was 10 calculated for every size class using Eqs. 9 and 10 from Kulmala et al. (2012). 11 The growth rates were also deduced for every size class, this was done separately for total 12 particles (GR t ) as well as positive (GR pos ) and negative ions (GR neg ). Growth rates were 13 determined using the maximum concentration method described in detail in section 6A by 14 Kulmala et al. (2012). In order to determine the point in time of the maximum concentration 15 (black filled circles in Fig. 2), we applied a least square polynomial smoothing filter (Savitzky 16 and Golay, 1964) to each of the NAIS size classes. Further smoothing of the determined times 17 of maximum concentration resulted in smooth size dependent growth rates (black curves in 18 Fig. 2). The determination of GRs from particle/ion measurements in the troposphere are 19 always associated with uncertainties (Yli-Juuti et al., 2011) as the growth of a particle 20 population is a dynamic process with several influencing factors. Therefore, the result of a GR 21 analysis from field measurements will always only result in an approximation of the true GR. 22 Besides, as the probability of particles carrying multiple charges in the NAIS increases with 23 particle diameter, the measured number size distribution for larger sizes is less reliable. 24 However, the growth rates for particles smaller than 20 nm in diameter give reasonable 25 results. For ion/particle diameters above 20 nm, the applied method results in an 26 overestimation of the growth rates (cf. Fig. 2). By comparing concentrations as well as growth 27 rates of total particles (Fig. 2 a) and neutral particles ( Fig. 2 b), it becomes evident that neutral 28 and total particles exhibit equivalent values. Therefore, data from the NAIS's total particle 29 measurements are used to describe neutral particle characteristics in the following. As the 30 same procedure was applied to all ion and particle measurements, the determined growth rates are well comparable. Further, a correction for self-coagulation of the growing mode was 1 applied to obtain the rates for pure condensational growth (Leppä et al., 2011). 2 3 3 Results 4

General event characteristics 5
Simultaneous measurements of neutral and charged clusters and particles at the "Waldstein" 6 ecosystem research site from 17 June to 18 August 2012 showed a frequent occurrence of 7 new particle formation events. Typically, the events occurred during sunny morning hours 8 while wind directions from the east prevailed. However, several events did also occur in the 9 afternoons and when wind directions were not from the east. A total number of 17 NPF events 10 (28 % of measurement period) were observed, while 29 days (47 %) could not be defined as 11 clear events but did still show particle formation. Non-event days were less frequent with only 12 15 out of 61 days. Since the measurements were taken at a fixed location, a reliable evaluation 13 of the patterns governing the formation and growth of particles were only possible in 14 homogeneous air masses. After careful evaluation for homogeneous air masses as described 15 above, a total of 8 events were chosen for detailed analysis. Fig. 2 shows a typical NPF event. 16 Growth rates of those 8 days compare well to prior observations, reporting growth rates in the 17 range from 2.2 to 5.7 nm h -1 at the same location (Held et al., 2004). For particles in diameter 18 range 2 -3 nm median total particle growth rates (GR t ), negative (GR neg ) and positive growth 19 rates (GR pos ) were found to be 4.1 nm h -1 , 2.4 nm h -1 and 2.8 nm h -1 , respectively. Median 20 formation rates J for 2-3 nm particles were in the order of 3.5 cm -3 s -1 , 0.015 cm -3 s -1 and 0.02 21 cm -3 s -1 for total, negative and positive particles, respectively. 22 23

Ion concentrations and ionization rates at "Waldstein" 24
The "Waldstein" site is located in the Fichtelgebirge mountain range, NE Bavaria. The 25 Fichtelgebirge is known for its enhanced background radioactive radiation levels. In 26 particular, radon is elevated, reaching soil gas activity concentrations of up to 4000 kBq m -3 27 (Kemski et al., 2001;Lüers et al., 2007). As the primary sources for atmospheric ions are 28 radon decay, gamma radiation and cosmic radiation (Hirsikko et al., 2011), ion concentrations 29 and ionization rates Q are expected to be elevated at the "Waldstein" site. The measurements with the NAIS in summer 2012 showed median concentrations of positive and negative 1 cluster ions on NPF event days of 339 and 148 cm -3 , respectively (cf. Tab. 1). The cluster ion 2 concentrations show a clear diurnal variation both on NPF event days and non-event days 3 (Fig. 3). Lüers et al. (2007) conducted radon measurements at the "Waldstein" site and found 4 similar diurnal patterns, hinting towards radon as the major ionization source. Furthermore, 5 our measurements show that cluster ion concentrations are slightly enhanced on NPF events 6 days (Tab. 1). Nevertheless, the concentrations seem quite low compared to values measured 7 at various locations around the world. Ion concentrations measured at 2 meter above ground The median ionization rates Q determined with the NAIS during NPF events are 0.8 and 28 0.9 cm -3 s -1 for negative and positive cluster ions, respectively (cf, Tab. 2). The calculated Qs 29 are most probably underestimated since Q depends directly on ion concentrations, which are 30 underestimated by the NAIS. Furthermore, the simplified balance equation for determining Q 31 does not consider all active ion sinks, resulting in a general underestimation of about a factor 32 of 2 (Hõrrak et al., 2008). Considering these facts, Q was probably much higher than 1 suggested by the NAIS measurements. 2 3

Time difference 4
In all 8 evaluated NPF events, 2 nm ions (NAIS size bin limits were 1.8 -2.1 nm) showed a 5 concentration increase before the concentrations of total particles of the same size increased. 6 Fig. 4 (a) shows the course of concentration for 2 nm total particles and ions for an exemplary 7 NPF event on 12 August, 2012. The occurrence of an earlier ion formation prior to total 8 particle formation seems to be a typical pattern during NPF. Manninen et al. (2010) report of 9 NAIS measurements during NPF at several locations in Europe. They also observed the 10 earlier formation of 2 nm ions prior to 2 nm total particle formation in different environments. 11 However, this behavior was not investigated in more detail in other studies. When considering 12 the concentrations of larger particles and ions, the time gap between the appearance of 13 charged and total particles becomes smaller with increasing particle size ( Fig. 4 b-e). This 14 behavior was observed throughout all NPF events considered in our study. In order to 15 determine the time difference ∆t between the appearance of ions and total particles, a cross-16 correlation analysis was performed individually for each size class. Cross-correlation analysis 17 is a standard procedure to analyze time shifts in two time series. The result of the cross-18 correlation analysis can be seen in Fig. 5. For small particles, ∆t is largest and sharply 19 decreases as the particle diameter increases, eventually reaching ∆t = 0 for diameters of about 20 20 nm. Therefore, the total particles seem to grow faster than ions after the onset of a NPF 21 event, as ∆t becomes smaller during the growth process. 22 23

Growth rates 24
Due to the decrease of ∆t during NPF, GR t is expected to differ from GR neg and GR pos , 25 especially when considering small particle diameters. In fact, our analysis yields an increased 26 GR t compared to GR neg and GR pos . At this point, it should be mentioned once more that the 27 growth rates above an ion/particle diameter of 20 nm are most probably overestimated by the 28 maximum concentration method. Fig. 6 (a) shows the growth rates for the NPF event on 4 29 July, 2012. GR neg and GR pos are similar to each other, while the total particles grow faster. 30 Fig. 6 (b) shows the median growth rates of all 8 regional NPF events. An enhanced GR t is 1 evident in the median values. The enhanced GR t compared to charged particle growth rates 2 deviates from theories for pure condensational growth, where the presence of a charge 3 enhances the growth rates of small and intermediate ions (e.g. Yu and Turco, 2000;Yue and 4 Chan, 1979). Therefore, condensational growth on its own cannot explain the apparent GR 5 differences. To further support our observations at the "Waldstein" site, we analyzed 6 additional data recorded with a NAIS instrument during summer 2008 at the "Melpitz" field 7 site in NW Saxony, Germany. In these data, the same patterns are found: ∆t decreases during 8 the growth process and total particles show an enhanced growth rate compared to ions. As the 9 determination of the growth rates is always connected to some error, the enhancement of GR t 10 over to GR neg and GR pos cannot be regarded as significant, but still it is considered to be 11 plausible. 12 13

Recombination 14
The number size distributions deduced from ion-ion recombination as described by Eq. 1 are 15 generally comparable to the measured total particle distributions. However, the resulting 16 absolute concentrations of particles from ion-ion recombination are one to three orders of 17 magnitude smaller than the observed total particle distributions. Particularly, when diameters 18 below 10 nm are considered, recombination cannot explain the abundance of total particles 19 (cf. Fig. 2). This may be partly due to the performance of the NAIS, as it generally 20 underestimates the ion concentrations and overestimates the total particle concentrations. 21 Therefore, the absolute values are not taken into consideration for our study. Nevertheless, the 22 recombination gives valuable information regarding the growth behavior of neutral particles. 23 A measure which can still be used for our analysis is the growth rate of the recombination 24 products (GR rec ). As mentioned above, GR t is elevated at small particle diameters compared 25 to GR neg and GR pos . GR rec seems to behave similar to GR t as can be seen in Figs. 2 and 6. For 26 most of the NPF events considered in our study, GR rec is well above GR neg and GR pos (Fig.  27 6 b) and sometimes matches GR t quite well (Fig. 6 a). 28 29 4 Discussion 1 The 8 particle formation events at the "Waldstein" site considered in this study can be 2 separated into two distinct stages. The formation of the first stable clusters and particles seem 3 to happen in the ion fraction. Later, the ion formation step is followed by a very intense 4 formation and growth of neutral clusters and particles. The initial ion induced nucleation (IIN)  5 typically happens about 20 -30 minutes before the first appearance of neutral particles (Fig. 5  6 c, d; Tab. 2) at "Waldstein". This observation can most likely be explained by the higher 7 stability of charged clusters over neutral ones at a certain precursor gas saturation ratio 8 (Enghoff and Svensmark, 2008;Yue and Chan, 1979). Furthermore, charged clusters clearly 9 activate more easily and grow more quickly (e.g. Lushnikov and Kulmala, 2004;Winkler et 10 al., 2008;Yu and Turco, 2000). Keeping this in mind and assuming no ion-ion and ion-11 particle interactions, the time difference between an earlier occurring ion fraction and the total 12 particle fraction during the growth process should increase or remain constant. However, our 13 measurements show a contrary behavior: once formed, the neutral particles grow considerably 14 faster than the ion fraction, and eventually, the earlier occurrence of the ions vanishes 15 completely. A possible explanation for the slower ion GR could be the diurnal variation of gas 16 phase precursors like sulfuric acid or oxidation products of volatile organic compounds 17 (VOC). In the early morning hours, when the first intermediate ions are formed, the precursor 18 gas concentrations are expected to be low. On sunny days, as were most of the considered 19 event days, the precursor gas concentration will increase during the day. This is due to 20 increasing VOC emissions from the forest with rising air temperature, as well as due to 21 photochemical processes leading to the formation of sulfuric acid and oxidation of VOCs. 22 Therefore, the neutral particle growth which occurs later could be enhanced due to higher 23 concentrations of precursor gases. 24 Additionally, ion-ion and ion-particle interactions enhance neutral particle GRs. As the 25 potential precursor gases were not measured in this study, the focus to explain our observation 26 will be on ion-particle interaction processes. Nevertheless, it is not expected that the 27 observations can be explained fully by ion-particle interactions. 28 Considering ion-particle interactions by applying theoretical parameterizations of the 29 attachment and recombination processes to the combined NAIS and mobility particle size 30 spectrometer measurements, we obtained the ion-mediated or -recombined fraction of neutral 31 particles. NAIS number concentration measurements are subject to uncertainties both for ions 32 and total particles (Asmi et al., 2009;Gagné et al., 2011 However, growth rate analyses are 1 not influenced by the uncertainties in NAIS number concentrations. Therefore, we chose 2 GR rec deduced from the calculated recombination number size distribution as a measure for 3 the influence of ions on neutral particle formation. 4 In general, our analyses show an earlier formation of charged particles compared to total 5 particles (Fig. 5). When looking more closely at the time difference of appearance (∆t) of ions 6 and total particles, the 8 considered NPF events can be divided in two classes: (1) initial ∆t is 7 larger than 20 minutes (Fig. 7) and (2) initial ∆t is smaller than 20 minutes (Fig. 8). 8 Median values of four NPF events (04 July; 23 July; 24 July; 12 August 2012; cf. Tab. 2) with 9 ∆t > 20 minutes are shown in Fig. 7. The large differences in the growth rates for ions and 10 total particles (Fig. 7 a) are remarkable. While GR neg and GR pos are as expected for small 11 diameters, GR t for small total particles is strongly elevated (cf. Tab. 2). This strong growth is 12 maintained until a sharp drop for diameters above 10 nm is evident. The unusual sharpness of 13 the decrease can most likely be attributed to limitations of the maximum concentration 14 method and the inversion routine of the NAIS. Nevertheless, qualitatively the decrease in GR t 15 is considered real, indicating a change in the prevailing growth conditions. Fig. 7 (b) shows 16 the time evolution of the growing mode's diameter of maximum concentration (Dp max ) for 17 both ion polarities as well as for total particles. More specifically, Dp max is the result of the 18 maximum concentration method for the determination of the growth rates (cf. black lines in 19 Fig. 2). The origin of the horizontal axis (time = 0) indicates the first appearance of the total 20 particle growing mode. The time of initial ion appearance is offset by the median of ∆t at 2 21 nm for positive and negative ions, respectively (cf. Fig. 7

c, d). The initial offset of the ion 22
growing mode is about 60 minutes. As total particles exhibit a higher GR t , their growing 23 mode finally reaches the same Dp max as the ion modes, about 40 to 60 minutes after the first 24 appearance of total particles. 25 particles. ∆t exhibits a rapid decrease as the particles grow. Eventually, for particle diameters 27 above 10 nm, the advance of ions is fairly small and continues to decreases at a slower rate, to 28 approach ∆t = 0 at about 20 nm. Additionally, Fig. 7

(c) and (d) show the independently 29
derived time difference between the negative and positive Dp max to the total one (cf. Fig. 7 c, 30 d as black dotted lines). Basically, this is a comparison of ∆t derived from the cross-31 correlation method with the time difference derived from the maximum concentration 32 method. The general patterns of these time differences are very similar: the rapid decrease of 1 ∆t is clearly evident until particle diameters of about 10 nm are reached. For greater particle 2 diameters the time differences of Dp max become negative, indicating a persistently enhanced 3 growth rate of the total particle growing mode. However, our data do not show an advance of 4 the total growing mode compared to the ion modes (cf. Figs. 4,5 and 7 c,d). This discrepancy 5 may be explained by the increasing uncertainty associated with the growth rate determination 6 for larger diameters. 7 Median values for four NPF events with ∆t < 20 minutes (17 June;19 June;13 August;17 8 August 2012;cf. Tab. 2) are shown in Fig. 8. The median growth rates for these events (Fig. 8  9 a) are significantly lower compared to the high growth rates presented in Fig. 7. Additionally, 10 there is no visible difference in GR neg , GR pos and GR t . They exhibit similar values throughout 11 the whole growth process (cf. Tab. 2). Typically, 2 nm positive and negative ions show an 12 earlier appearance (∆t) of about 15 and 10 minutes, respectively (Fig. 8 c, d). The decrease of 13 ∆t during the growth process is relatively slow. Nevertheless, the diameter at which ∆t 14 approaches zero is still at about 20 nm. The time needed for the total particle mode to grow to 15 this size is approximately 200 minutes (Fig. 8 b). The time difference deduced from Dp max 16 becomes negative at a diameter of about 20 nm, supporting the assumption that growth rates 17 above this diameter are overestimated. As ∆t shows a slow decrease during the growth 18 process, GR t should be slightly enhanced compared to GR neg and GR pos . This is not visible in 19 our data. Presumably, the accuracy of the applied growth rate determination is not sufficient 20 to resolve such slight differences. 21 As the absolute contribution of ion-ion recombination and ion-particle attachment to NPF is 22 not quantitatively assessed in this work we propose a conceptual mechanism governing our 23 observations. Fig. 9 shows the conceptual model for interactions of positive cluster ions (red) 24 with the negative growing ion mode (blue), the neutral background particles and the neutral 25 growing mode (both black). For illustrational purposes, we will focus on the ion attachment 26 (green dashed lines) and the recombination of cluster ions with the growing ion mode (yellow 27 dashed lines) and neglect the recombination of cluster ions with each other. 28 At the onset of NPF (Fig. 9 a), first particles are formed in the ion fraction, exhibiting 29 concentrations in the order of 10 1 cm -3 . Ion-ion recombination occurs among cluster ions and 30 the freshly nucleated ion mode (yellow dashed line). Additionally, the background aerosol 31 particles, exhibiting concentrations in the order of 10 3 cm -3 , are available for the attachment of 32 cluster ions (green dashed line). Considering the recombination coefficient ߙ at 2 nm and the 1 attachment coefficient ߚ at 100 nm (cf. Fig. 1, yellow and green solid lines), the probabilities 2 for cluster ions to interact with the growing ion mode and with the neutral background 3 particles are approximately the same. As the background aerosol is more numerous than the 4 freshly nucleated ion mode, attachment to the background particles dominates over 5 recombination. Hence, only a very small number of neutral particles are formed by 6 recombination. 7 Once precursor gas phase components are available in a sufficient quantity for neutral 8 nucleation (cf. Almeida et al. 2013;Kulmala et al., 2013;Schobesberger et al., 2013), a strong 9 nucleation burst of neutral particles occurs (Fig. 9 b). The freshly nucleated neutral mode has 10 a very small mean diameter (e.g. 1.5-2 nm) and shows typical concentrations in the order of 11 10 3 cm -3 . The background particle number size distribution stays mostly unchanged (Dp > 100 12 nm; 10 3 cm -3 ). Now, the neutral nucleation mode and the background particles are available 13 for the attachment of cluster ions. Meanwhile, the ion mode has grown to a greater diameter 14 (e.g. 4 nm), exhibiting only a slightly enhanced number concentration still in the order of 15 10 1 cm -3 . ߚ for cluster ion attachment to the background particles is elevated by 2 orders of 16 magnitude compared to the neutral nucleation mode (cf. Fig. 1). Therefore, cluster ion 17 attachment to the background particles dominates over the attachment to the neutral 18 nucleation mode, as both modes have similar concentrations. On the other hand, ߙ for cluster 19 ions with the growing ion mode is elevated by 2 orders of magnitude compared to ߚ for the 20 neutral growing mode. As the neutral mode exhibits approximately 2 orders of magnitude 21 more particles, the absolute number of cluster ions recombining with the ion mode is 22 comparable to the number of ions attaching to the neutral mode. In other words, background 23 particles are charged strongly (bold red arrow), the neutral nucleation mode experiences 24 moderate charging (red arrow) and the formation of neutral particles by recombination is also 25 moderate (black arrow). This moderate formation of somewhat greater neutral particles from 26 recombination contributes to the growth of the neutral mode. On the other hand, the ions 27 formed by attachment to the neutral mode are somewhat smaller than the mean ion mode 28 diameter, and contribute to a slower growth of the ion mode. The absolute production of 29 neutral and charged particles by this mechanism depends on the concentration of cluster ions 30 as well as on the concentration of the growing ion-and neutral modes, and is thought to be in 31 the order of 0.01 cm -3 s -1 . 32 As the growth continues, the neutral particle mode reaches a number concentration peak 1 (order of 10 4 cm -3 ) at diameters of approximately 4 -5 nm (Fig. 9 c). Due to the high 2 concentration, the attachment probability of cluster ions to the neutral nucleation mode and 3 the background particles is similar (green dashed lines). Meanwhile, the ion mode has grown 4 further (e.g. 6 nm diameter), and is slightly more numerous but still in the order of 10 1 cm -3 . 5 Therefore, recombination is somewhat enhanced compared to stage (b). Nevertheless, the 6 neutral nucleation mode experiences a stronger loss of particles due to attachment of cluster 7 ions. As a result, the concentration of the growing ion mode is further enhanced by the 8 addition of somewhat smaller charged particles. Again, the loss of ions (due to 9 recombination) and the addition of newly formed smaller ions (due to attachment) results in 10 an apparent growth rate reduction of the ion mode. On the other hand, the concentration of the 11 neutral mode is constantly reduced, while its growth rate stays elevated. 12 Finally, the diameters of the neutral and ion growing modes approach each other ( Fig. 9 d). 13 By this time the concentration of the ion mode is further enhanced (10 2