Model studies on ion-induced nucleation in the atmosphere

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D20, 4427, doi: /2002jd002140, 2002 Model studies on ion-induced nucleation in the atmosphere L. Laakso, J. M. Mäkelä, 1 L. Pirjola, and M. Kulmala Department of Physical Sciences, University of Helsinki, Helsinki, Finland. Received 28 January 2002; revised 18 April 2002; accepted 30 April 2002; published 23 October [1] A new model for ion-induced nucleation and charged aerosol dynamics is presented in this paper. It was found that ion-induced nucleation is able to produce a considerable amount of new particles if the preexisting particle concentration is sufficiently low. Also, when only positive or negative ions nucleate a large amount of particles in observable sizes was produced. It was also found that there can be continuous nucleation in particle sizes below the detection limit of most commonly used aerosol instruments at low temperatures and high preexisting particle concentrations. In some simulated conditions, fair agreement with observed particle formation events in boreal forest environment was achieved. According to the results, in certain situations ion-induced nucleation changes the charge distribution of the particles, which may allow the observation of ion-induced nucleation in the atmospheric conditions. INDEX TERMS: 0305 Atmospheric Composition and Structure: Aerosols and particles (0345, 4801); 0365 Atmospheric Composition and Structure: Troposphere composition and chemistry; 4842 Oceanography: Biological and Chemical: Modeling; KEYWORDS: ioninduced nucleation, nucleation, atmospheric nucleation, ions, changed aerosol particles, aerosol particles Citation: Laakso, L., J. M. Mäkelä, L. Pirjola, and M. Kulmala, Model studies on ion-induced nucleation in the atmosphere, J. Geophys. Res., 107(D20), 4427, doi: /2002jd002140, Introduction 1 Also at Institute of Physics, Tampere University of Technology, Tampere, Finland. Copyright 2002 by the American Geophysical Union /02/2002JD [2] In the atmosphere, 3 nm particle formation has been observed in different environments; Mäkelä et al. [1997] measured new nanoparticles in continental site of Hyytiälä, Finland, Hõrrak et al. [1998] made similar observations in Estonia, and Weber et al. [1997] in remote continental site in Central USA. There are also several observations in marine air [Covert et al., 1992; O Dowd et al., 1999] as well as in the free troposphere [Weber et al., 1999]. [3] Although bursts of new particles have been observed, the mechanism of particle formation still remains unclear. Several nucleation mechanisms have been proposed, these include classical binary homogeneous nucleation [Seinfeld and Pandis, 1998], ternary nucleation [Kulmala et al., 2000b], ion-induced nucleation [Raes and Janssens, 1985; Raes et al., 1986] as well as ion-mediated nucleation [Yu and Turco, 2000]. None of the mechanisms has been confirmed or rejected yet. If the different mechanisms are compared, ternary nucleation seem to be most effective way of produce new particles [Kulmala et al., 2000a]. It is also possible that there are several nucleation mechanisms taking place either simultaneously or separately in the atmosphere. [4] In this article we concentrate mainly on ioninduced nucleation. According to the laboratory measurements the presence of ions accelerate nucleation rate with several orders of magnitude [Kim et al., 1997]. Theoretically, the electric interaction between the ions and condensing vapor lowers the free energy needed for cluster formation. Because of this, it has been suggested that new particles can be formed via ion-induced nucleation, specially in places where the ion production rate is high like in the upper atmosphere [Seinfeld and Pandis, 1998]. [5] However, there are certain problems related to ioninduced nucleation. In the lower atmosphere the ion production rate is often too low to allow nucleation rates calculated from the observations [Dal Maso et al., 2002]. To get the observed particle formation rates at measurement limit (3 nm diameter) the real nucleation rate (at about 1 nm) in homogeneous nucleation has to be about cm 3 s 1 [Kulmala et al., 2001b; Dal Maso et al., 2002] in forest sites and much higher, cm 3 s 1, in coastal sites. The limiting factor is thus the ion production rate, which in the lower atmosphere is normally less than 10 cm 3 s 1. [6] One possible explanation is presented by Yu and Turco [2000]. They assume that the particles grow via ion-mediated nucleation. In the proposed mechanism, the condensation onto charged particles is enhanced by Coulomb interaction. If the condensation rate is high enough, even lower nucleation rates may produce a considerable amount of new particles. However, in coastal sites ions can not be the main reason for nucleation. [7] There are also other competitive theoretical explanations for nucleation events. One of these is based on socalled thermodynamically stable clusters [Kulmala et al., 2000b]. These are small stable clusters, which act as small condensation nuclei. If this explanation is correct at least in some cases, these clusters would have an effect on ions AAC 5-1

2 AAC 5-2 LAAKSO ET AL.: ION-INDUCED NUCLEATION and their properties. This imposes an interesting task for future studies. [8] In this paper we present a full aerosol model which can be used in investigations of ion-induced nucleation in the atmosphere as well as in experiments. The model can also be applied on calculations of charged particle coagulation and bipolar charging. The model includes binary sulfuric acidwater nucleation, condensation, coagulation with electric interaction forces and ion attachment onto aerosol particles. [9] The model is explained in detail in the next section. First an overview of the model is given. In subsection 2.1, the principles of ion-induced nucleation are explained. In subsection 2.2, the calculation of condensation is presented. The coagulation with Coulomb interaction is discussed in subsection 2.3. Subsection 2.4 contains the calculations of ion-aerosol attachment coefficients. All the above terms are combined into general dynamic equation (GDE) in subsection 2.5. In section 3, main results from 120 model runs are given and some interesting cases are analyzed in detail. Section 4 summarizes the results. 2. The Model [10] The model is originally based on a sectional model AEROFOR [Pirjola, 1999]. The particle size range in the present model covers particles having radii between 0.5 and 1000 nm. Particles between 0.5 and 1 nm are divided in 10 size classes enabling the simulation of the dynamics of small ions in ion-induced nucleation. The rest of the size range is divided logarithmically in 27 size classes. All size classes under 10 nm are also divided in 3 charge classes corresponding 1, 0, and +1 charged particles. Three charge classes are chosen, because these small particles are too small to carry more than one charge [see, e.g., Wiedensohler et al., 1986]. [11] Size classes for bigger particles are divided to 11 classes, from 5 to +5 elementary charges. The number of size and charge classes is arbitrary as well as the maximum size of particles. The values used here are chosen so that they describe the system well enough but are not calculationally too heavy. [12] Besides the particle size classes, two more classes are allowed for ions smaller than 0.5 nm. Ions in these two classes act as initial ions in ion-induced nucleation. They are also able to attach on aerosol particles. Here a separation between particles and ions is based on critical radii in ioninduced nucleation. If the particles are bigger than larger of the two critical radii, they are considered as charged particles, otherwise as ions. [13] This model provides a simple water-sulfuric acid chemistry. Processes modifying the particles size and charge distribution include coagulation with interparticle forces, condensation with enhancement due to the image forces, ion-induced nucleation as well as the attachment of ions on aerosol particles. The model as a whole is build such a way that it can be applied to different temperatures and pressures. For this purpose, the properties of small ions can also be modified Ion-Induced Nucleation [14] Classical ion-induced nucleation theory in binary system states that in a closed system containing an ion with charge q and radius r 0 the Gibbs free energy of a liquid cluster formation is given by the following expression [Yue and Chan, 1979]: Gðn a ; n b Þ ¼ n a kt ln A ag A al þ 4pr 2 s þ q2 8p 0 n b kt ln A bg A bl r r 1 r 0 where r is the radius of the cluster, s is surface tension, 0 is vacuum permittivity, r is relative permittivity, k is the Boltzmann constant, T is the temperature, A ag and A bg are the activities of substances a and b in gas phase, A al and A bl are the activities of substances a and b in liquid phase. n a and n b are the numbers of molecules of the substances and q is the charge of the initial ion and r 0 the corresponding radius. The radius r is given by ð1þ 4 3 p r3 r0 3 r ¼ na m a þ n b m b ð2þ where m a and m b are the masses of the molecules and r is the density of the solution. With capillarity approximation and Gibbs-Thompson equation the critical radii and the mass fraction X at the saddle point can be solved from the expression: ln Aag A al ¼ v a ln Abg v b A bl where v a and v b are the molecular volumes of substances a and b v a ¼ m a r v b ¼ m b r 1 þ r@x 1 1 r@x ð3þ ð4þ : ð5þ The calculations can be simplified by using the concept of virtual molecule [Kulmala et al., 1991]. In this case the volume of the virtual molecule is v ¼ X 0 v a þ ð1 X 0 Þv b : ð6þ where the mole fraction X 0 is given by n b X 0 ¼ n a þ n b Using this method the critical radius r* is: 2 3 r* ¼ 2sv e kt ln S 1 4 r 5; 64p 2 0 sr* 3 ð8þ where the virtual saturation ratio S is S ¼ A 1 X 0 ag A bg A al A bl X 0 : ð7þ ð9þ

3 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC Critical radii [m] r 3 r 2 r 1 One solution Two solutions Zero solutions Sulphuric acid concentration Figure 1. Solutions for equation (8). If sulphuric acid concentration is very low, equation has only one solution. If sulphuric acid concentration is over certain limit, equation have no solutions. Between these two ends it has two solutions. Critical radii for homogeneous nucleation is also shown for comparisons. Equation (8) can be solved by iteration. Depending on sulfuric acid concentration, it has either 0, 1, or 2 solutions as shown in Figure 1. [15] If the number of solutions is two, the energy barrier for ion-induced nucleation is dg ¼ 4p r3 2 r3 1 r=3 ð1 X 0 Þm a þ X 0 kt ln S þ 4ps r2 2 m r2 1 b þ q ; ð10þ 8p 0 r r 2 r 1 where r 1 and r 2 are the solutions of equation (8). The nucleation rate is given by I ¼ R av n Z expð dg=ktþ; ð11þ where n ± is the concentration of positive or negative ions, R av the average condensation rate, and Z is the Zeldowich nonequilibrium factor given by Stauffer [1976] and Kulmala and Viisanen [1991]: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 1 q2 ð1 u 1 rþ t 64p 2 0sr2 3 v Z ¼ kt 2pr2 2 ð12þ Excluding hydrates, the average condensation rate R av is [Kulmala and Laaksonen, 1990] where q is the angle between nucleation current and n b -axis in Gibbs free energy surface and R aa and R bb are the condensation rates of a and b [McGraw and Laaksonen, 1997] rffiffiffiffiffiffiffiffiffiffiffi R aa ¼ c a r2 2 8pkT m a sffiffiffiffiffiffiffiffiffiffiffi R bb ¼ c b r2 2 8pkT ; m b ð14þ where c a and c b are the concentrations of substances. The problem in the classical ion-induced nucleation theory is that it does not take into account the sign-preference of ioninduced nucleation [Seinfeld and Pandis, 1998]. This difference in nucleation rates is assumed to result from the effect of dipole moment and can not be described by classical nucleation theory [Kusaka et al., 1995] Condensation [16] Condensation rate of sulfuric acid on aerosol particles is given by Kulmala [1990] and Pirjola and Kulmala [1998] C cond ¼ AC i N i c b ; ð15þ where N i is the particle number concentration in size class i, A is the enhancement factor due to the image forces between a particle and condensing vapor molecule and C i is the condensation coefficient. R av ¼ R aa R bb R aa sin 2 q þ R bb cos 2 q ; ð13þ C i ¼ 4pR i b M ð16þ

4 AAC 5-4 LAAKSO ET AL.: ION-INDUCED NUCLEATION The transitional correction factor b M is [Fuchs and Sutugin, 1971] K n þ 1 b M ¼ 0:377K n þ 1 þ 3 4 a 1 Kn 2 þ 3 ; ð17þ 4 a 1 K n where a is the sticking probability (in this work a =1). Knudsens number K n is K n ¼ l b R i ; ð18þ where the mean free path of the sulfuric acid molecules, l b, is given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffi pm b l b ¼ 3 8kT D b ð19þ [17] Diffusion coefficient of vapor molecule [Reid et al., 1987] is D b qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T 1:75 1 m air þ 1 m b D b ¼ 2 ð20þ p d 1=3 air þ d 1=3 b where m air is the mass of air molecule and d air and d b the diameters of air and acid molecules. Enhancement factor A is calculated according to [Hoppel and Frick, 1986] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 pq A ¼ 1 þ 2 2 4p 0 8R i kt ð21þ This approximate enhancement factor is actually valid for ion-neutral aerosol attachment. When it is used as an enhancement factor between a charged particle and a neutral molecule it somewhat overestimates the effect of image forces Coagulation [18] Coagulation is considered as collisions between neutral or charged particles. Ion collisions with aerosol particles, i.e., ion-aerosol attachment, is explained more in detail in the next chapter. The coagulation term is presented by dni l ¼ Kij lm Ni l dt N j m ð22þ where K is the coagulation coefficient and N the particle number concentration. Superscripts refer to charges and lm subscripts to particle sizes. Coagulation coefficients K ij between the particles of size i and j are calculated from the expression of Fuchs [1963, 1964] where R ij is R i + R j, relative particle diffusion q coefficient D ij = D i + D j and relative velocity v ij ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi v 2 i þ v 2 j. Thermal velocity of a particle of size i is given by sffiffiffiffiffiffiffiffi 8kT v i ¼ pm i ð24þ where m i is the mass of the particle. The flux-matching distance d ij is calculated according to Fuchs [1964] and Pirjola and Kulmala [1998]. The correction factor a lm ij due to the Coulomb and van ver Waals forces is calculated according to Howard et al. [1972], Ball and Howard [1971], and Mick et al. [1991] a lm ij ¼ b 2 crit ð25þ R ij where b crit is calculated in the case of repulsive Coulomb potential from b crit ¼ exp½ fðr m Þ=kTŠ ð26þ and in all other cases (including one neutral and one charged particle) b crit ¼ rm 2 ð 1 f ð r mþ=ktþ: ð27þ r m is the value in which equation (27) has its minimum value. In repulsive case, equation (26), r m is the value where potential f has its maximum value. The potential f(r) is fðþ¼f r C ðþþf r VdW ðþ r ð28þ where f C (r) is due to the Coulomb force and f VdW (r) is due to the Van de Waals-forces. Van der Waals potential is given by " f VdW ðþ¼ r A H 2R i R j 2R i R j 6 r 2 2 þ R i þ R j r 2 2 R i R j r 2 2!# R i þ R j þ ln r 2 2 ð29þ R i R j where A H is the Hamaker constant. The electrostatic potential is f C ðþ¼ r r 1 e 2 0 ðp ii 1=R i Þz 2 i þ 2p ij z i z j þ p jj 1=R j z 2 r þ 1 8p j 0 ð30þ where p ii = q jj /C, p jj = q ii /C, p ij = q ij /C. C is given by where C ¼ q ii q jj q 2 ij ð31þ K lm ij ¼ a lm ij 4pD ij R ij R ij R ijþd ij þ 4Dij v ijr ij ð23þ q ii ¼ R i ð1 hþ X1 q m = 1 hq 2m m¼0 ð32þ

5 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC 5-5 q jj ¼ R j ð1 bþ X1 q m = 1 bq 2m m¼0 ð33þ X 1 q ij ¼ R i R j =r 1 q 2 q m = 1 q 2mþ2 ð34þ m¼0 p where h =[(R i + R j q)/r] 2, b =[(R j + R i q)/r] 2, q ¼ g ffiffiffiffiffiffiffiffiffiffiffiffiffi g 2 1 and g = (r 2 R 2 i R 2 j )/2R i R j. The calculation of the coagulation coefficient between particles is adapted here from Yu and Turco [1998] with a modification in the calculation of the coagulation correction factor. While Yu and Turco used a correction factor taken from Fuchs [1964], our correction factor is taken from Howard et al. [1972] and Mick et al. [1991]. In Fuchs approach, the correction factor is calculated from diffusion-mobility equation in continuum regime whereas our approach emphasizes the kinetic regime. However, the resulting correction factors are close to each other Ion-Aerosol Attachment Coefficients [19] The aerosol attachment coefficients are calculated according to Fuchs [1964]. The attachment coefficients are given by where h i 4pR i D ion ¼ h ð35þ 4D ionr i exp fd ðþ a ioncd 2 kt iþ C d C d ¼ R i Z 1 d 1 r 2 exp fr ðþ dr kt The radius of limiting sphere d is given by d ¼ R3 i 2 l ion " þ l 5 ion 1 R i þ 2 5=2 # 15 1 þ l2 ion R 2 i 3 1 þ l2 ion R 2 i 1 þ l ion R i ð36þ ð37þ The potential f ion (r) between an ion and an aerosol particle is f ion ðþ¼ r e2 0 4p 0! z i r r 1 R 3 i r þ 1 2rðr 2 R 2 i Þ ð38þ where r a is the apsidal distance. In the above equations the velocity of an ion is given by the ion diffusivity sffiffiffiffiffiffiffiffiffiffiffi v ion ¼ 8kT ; ð41þ pm ion and the mean free path of the ion D ion ¼ mkt e 0 ; ð42þ mm air v ion l ion ¼ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð43þ 0:75e 0 1 þ mair where m is the mobility of the ion. Use of equation (8) to determine ion sizes would lead into equal sized positive and negative ions. Therefore the values given by Hoppel and Frick [1986] have been taken. This is also more realistic, when comparing with measured values e.g., in the background air [Hõrrak, 2001] General Dynamic Equation [20] The aerosol dynamical mechanisms presented above form together a set of differential equations, so-called General Dynamic Equation (GDE) [Pirjola, 1999; Raes and Janssens, 1986] dn q i dt m ion ¼ I qn* n i 1 d n i n n*; ½n i 1;n i Š þ I qn iþ1 n* d i 1 n iþ1 n n*; ½n i;n iþ1 i þ AC i 1 N q i 1 n i n ðþc t bðþ t AC i N q i ðþc t b ðþ t i 1 n iþ1 n i þ Xqmax X i X i l;m ¼ qmin j ¼ 1 k ¼ j d njþn k; ½n i 1;n i Šd lþm;q þ Xqmax X i X i l;m ¼ qmin j ¼ 1 k ¼ j d njþn k; ½n i;n iþ1 Šd lþm;q N q t K l;m j;k i ðþ Xqmax Xnclass K q;p i;j N p j p ¼ qmin j ¼ 1 Nj l ðþn t k m 1þd j;k d l;m ðþ t n j þ n k Š ni 1 ðn i n i 1 Þ K l;m j;k Nj l ðþn t k m ðþ t ðn iþ1 n j þn k 1þd j;k d l;m ðn iþ1 n i Þ ðþþh t q 1 i;þ nþ N q 1 i ðþ t The Fuchs a ion -coefficient is defined as þ h qþ1 i; n N qþ1 i ðþ h t q i; n N q ðþ h t q i;þ nþ N q ðþ t i i ð44þ a ion ¼ b 2 min ð39þ d in which the minimum impact parameter b min is obtained from the minimum of equation b 2 ¼ ra 2 1 þ 2 ½ 3kT f ionðþ f d ion ðr a ÞŠ ð40þ where subscripts refer to sizes and superscripts to charges. I q l, is the nucleation rate, C i the condensation rate and K m j, k is the coagulation coefficient between particles of size j and k with charges l and m and A is the enhancement factor in condensation due to the image forces on charged particle. h q i, ± is the attachment coefficient between ions and aerosol particles and n + and n are the number concentrations of positive and negative ions. nclass is the number of size classes and qmin and qmax are the lower and upper limits of charge classes in corresponding particle sizes as described

6 AAC 5-6 LAAKSO ET AL.: ION-INDUCED NUCLEATION in the beginning of this section. This equation is valid for particles that are bigger than the critical radii for neutral nucleation. The first line presents particles formed via ioninduced nucleation, second line particles coming to size class i via condensation, the third and forth line source from coagulation and the fifth line the loss of particles caused by coagulation. The sixth and the seventh line are the source and sink terms because of ion-aerosol attachment. The reason for having two terms in each cases except coagulation loss is that the particles coming between size classes are divided between two closest size classes. Because of this, the size class i gets particles from the size interval [i 1, i] and [i, i +1]. [21] Kronecker s delta function is described in previous equation as ½ Š ¼ 0; n j þ n k =2 ½n i ; n iþ1 Š 1; n j þ n k 2 ½n i ; n iþ1 Š d njþn k; n i;n iþ1 and with respect to charges, 0; l 6¼ m d l;m ¼ 1; l ¼ m [22] The equation of continuity for sulfuric acid is dc b ðþ t ¼ Q b X1 n* ;q I q c b ðþ t Xqmax Xnclass C i N q i dt q ¼ 1 q ¼ qmin i ¼ 1 þ Xqmax X i X i l;m ¼ qmin j ¼ 1 k¼j þ h 1 i;þ nþ Ni 1 K l;m j;k Nj l ðþn t k m ðþd t 1 þ d j;k d njþn k2 0;n 0; l;m ½ * Š d lþm;0 þ hi; þ1 n Ni þ1 d njþn k2½0;n 0; * Š ð45þ where subscript n i refers to the number of sulfuric acid molecules in particle of size class i. n*,0 is the critical number of sulfuric acid molecules in homogeneous nucleation of binary water-sulfuric acid system. n*,±1 corresponds to the bigger of the two critical radii in ioninduced nucleation. The first term on the right hand side in equation (45) represents the sulfuric acid production rate, the second one sulfuric acid lost by nucleation. The third term presents sulfuric acid used by condensation. The fourth term is a source term from coagulation in cases where the resulting neutral particle s radius is smaller than critical radii in homogenous nucleation. These particles are assumed to be unstable and thus evaporate. The last term is similar to the second last, but in this case the unstable particles are formed from ion-particle collisions. [23] The balance equation for small positive and negative ions is dn ðþ t ¼ Q I a rec n n n Xnclass dt i ¼ 1 Xqmax p ¼ qmin h p i; N p i ð46þ where a rec is the ion-ion recombination coefficient and Q ± the ion production rate. The first term on the right hand side is the ion production rate and the second one sink describes a sink due to the ion-induced nucleation. The third term is because of ion-ion recombination and the fourth term is caused by ion-aerosol particle attachment. 3. Results [24] Because such a big model easily includes a lot of errors, the results from coagulation, condensation and neutral nucleation were compared with the mother-model AEROFOR. Also, the charged fraction resulting from the ion-aerosol attachment was compared with measurements. In addition to that, the conservation of mass and charge were checked. [25] We would also have been able to include binary homogeneous nucleation here, so that two nucleation mechanisms would have been able to act simultaneously. In certain cases when condensation sink is low i.e., for low preexisting particle concentrations or for low ion production rates, homogeneous and ion-induced nucleation may occur simultaneously. However, as Kulmala et al. [2000a] have shown, this situation is often quite improbable. [26] Parameters for ions, preexisting particle concentrations and sulfuric acid-water chemistry used in our calculations are given in Table A1 in Appendix A. The properties of the positive and negative ions have been taken from Hoppel and Frick [1986]. The values for mobilities used here are lightly smaller than the observations suggest. Also the ion-ion recombination coefficient was taken from the literature. The value given corresponds to ion masses but not exactly the mobilities. This is a small discrepancy, but it does not change the results, because the sink of ions by aerosol particles is an order of magnitude higher than the sink by recombination [Laakso et al., 2000]. [27] The sensitivity of the model on ion properties was also checked. We used in this analysis ion mobilities (m + = and m = m 2 /V/s) measured by Hõrrak [2001] and masses (195 and 140 amu) and recombination coefficient ( m 3 /s) calculated from the measurements. It was found that in most of the cases change in final particle concentration was only a few percentages and always less than 10 percentages. The differences were biggest with low nucleation rates. [28] Our main interest was to investigate different nucleation situations and the effect of preexisting aerosols on ion-induced nucleation. For this purpose we have calculated the behavior of aerosol particles in two different temperatures, 273 and 293 K and in two different relative humidities, 50% and 90%. We chose these relative humidities and temperatures to correspond approximately the range springtime conditions in Hyytiälä measurement station [Kulmala et al., 2001a]. Springtime is of our interest because most of the nucleation events occur in March, April, and May. [29] In addition to this, we have simulated two different types of ion-induced nucleation, namely a symmetric case where both positive and negative ions nucleate and an asymmetric case where only negative ions nucleate. This is done because according the measurements the negative

7 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC 5-7 T=273 symmetric T=273 asymmetric, all Clean moderate RH50 Dirty RH90 T=293 symmetric T=293 asymmetric Figure 2. Final concentrations. Curves with different line style present three different preexisting particle concentrations as defined in Appendix A: solid lines clean air, dashed lines moderate air and dash-dot line dirty air. Lines with and without dots are relative humidities of 50% and 90%, respectively. ions may nucleate more easily than the positive ions. In all model runs sulfuric acid production rate was kept constant. [30] We have also done all the calculations for five different ion production rates to see what kind of differences it makes on the results. The ion production rate in Finnish conditions is between 2 and 10 cm 3 s 1. About half of the ions are produced by galactic cosmic rays, the rest comes from the decay of radioactive material in the air. Close to the ground, decay of tracer gas Radon can be the main source of ions. [31] Figure 2 shows the total final particle concentration after 4 hours resulting from 120 separate model runs. In these four subfigures two on left present symmetric nucleation and two on right asymmetric. In the upper figures temperature was 273 K and in the lower figures 293 K. Curves with different line style represent three different preexisting particle concentrations: solid lines Clean air, dashed lines Moderate air and dash-dot line Dirty air as defined in Table A2 in Appendix A. Lines with and without marker dots are relative humidities of 50% and 90%, respectively. The y axis marks the total particle concentration after 4 hours and the x axis the ion production rate. [32] From upper left figure it can be seen that occurrence of nucleation is independent of preexisting particle concentration at this temperature. The effect of preexisting particles on final concentration is due to the difference in coagulation and condensation. The main difference between dirty and two other cases is caused by coagulation to larger particles as can be seen by comparing this figure with Figures 3 and 4. In all of the cases at this temperature the nucleation is limited by ion production rate. The difference in final particle concentration results from differences in coagulation. [33] It is interesting to note, that the resulting particle concentration is in asymmetric nucleation as high as it is in symmetric nucleation. There are two reasons for this. If ions of only one sign nucleate, the concentration of sulfuric acid grows. This means that the condensation is accelerated. When concentration is faster, small particles have less time to coagulate, so the resulting amount of particles is higher. Another reason is that when only negative ions nucleate, the ions of opposite sign neutralize newly nucleated particles. If ions of both signs nucleate, resulting particles are neutralized by particles of opposite sign, and thus for each neutralization event one particle is lost. This is contradictory to the previous case where particles are neutralized by ions.

8 AAC 5-8 LAAKSO ET AL.: ION-INDUCED NUCLEATION T=273 symmetric T=273 asymmetric, >3nm Clean moderate RH50 Dirty RH90 T=293 symmetric T=293 asymmetric Figure 3. Final concentrations of particles with diameter greater than 3 nm. Labels as in Figure 2. T=273 symmetric T=273 asymmetric, >10 nm Clean moderate RH50 Dirty RH90 T=293 symmetric T=293 asymmetric Figure 4. Final concentrations of particles with diameter greater than 10 nm. Labels as in Figure 2.

9 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC 5-9 Figure 5. Particle concentration as a function of time, particle radius and particle charge. Logarithmic particles concentration scale is shown at the bottom of the picture. In the figure upper left there are negatively charged particles and in the upper right neutral particles. Two figures at the bottom represent positive particles and the sum of all particles with different charges in each size. The initial conditions for this picture have clean preexisting size distribution, temperature is 293 K, relative humidity is 50% and the ion production rate 10 ion pairs/cc/s. The nucleation is considered asymmetric because only negative ions nucleate. [34] In the lower pictures preexisting particle concentrations prevent ion-induced nucleation in case of dirty air. Otherwise the curves are as to be expected: in case of high relative humidity all ions nucleate. In case of RH 50% the effect of preexisting particle concentration can be seen more clearly. Also, here both symmetric and asymmetric cases result approximately the same final particle concentration with slight benefit for symmetric case. It can also be noted that at lower temperature the particles grow in lower relative humidity more than in higher relative humidity. In higher temperatures the situation is the opposite. [35] Four main phenomena favoring the formation of particles can easily be seen from these pictures. Namely, low preexisting aerosol particle concentration, high relative humidity, low temperature, and high ion production rate. [36] The final concentration of particles with a diameter greater than 3 and 10 nm are shown in Figures 3 and 4, respectively. It can be seen from the upper two subplots that in the case of dirty air, particles do not grow to measurable sizes but they coagulate very rapidly. Common to all temperatures and relative humidities, it is possible to observe nucleation if the preexisting particle concentration is clean or moderate. It can be seen from Figure 4 that in clean air the particles are able to grow easier than in moderate air. Comparing these result with observations made in e.g., in Mace Head [O Dowd et al., 1999; Dal Maso et al., 2002], it can be seen that the particles can not be formed via ion-induced nucleation, except if the ion production rate is extraordinary high. The situation is different in Hyytiälä, where the ions could in principle trigger the particle formation. [37] In addition to final concentrations we consider more in detail three different interesting nucleation occasions: [38] In case 1 the preexisting particle concentration is clean, as described in Appendix A. Temperature is 293 K, relative humidity 50%, ion production rate 10 ion pairs per cubic centimeter per second and the nucleation is considered asymmetric. In this case only the negative ions nucleate. However, due to positive ions fresh nanoparticles will be neutralized very rapidly. They can even be charged

10 AAC 5-10 LAAKSO ET AL.: ION-INDUCED NUCLEATION Figure 6. Total particle concentration, number of sulphuric acid molecules and the concentration of negative and positive ions as a function of time. Initial conditions are same as in Figure 5. Nucleation rate 1/cm 3 /s T=293, RH=50 Q=10, Asymmetric Clean Time [s] Critical radius [m] Time [s] Figure 7. 5 and 6. Nucleation rate and critical radii r 2 from equation (8). Initial conditions are same as in Figures

11 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC Negative Neutral 10 7 T=293, RH=90 Q=10, Symmetric Clean Radius [m] 10 8 Radius [m] Time [h] Time [h] 10 6 Positive 10 6 Total Radius [m] Radius [m] Time [h] Time [h] dn/dlog(r p ) Figure 8. Particle concentration as a function of time, particle radius and particle charge. The initial conditions for this picture have clean preexisting size distribution, temperature is 293 K, relative humidity is 90% and the ion production rate 10 ion pairs/cc/s. The nucleation is symmetric. For more details, see Figure 5. positively as can be seen from Figures 5 7. During the nucleation there is a huge difference between concentration of positive and negative ions. The nucleation rate is peaking in the beginning of the period but as soon as the preexisting ions are used, nucleation rate is limited by ion production rate. When the sulfuric acid concentration decreases, also nucleation rate decreases. Nucleation radii r 2 has its minimum when sulfuric acid concentration has its maximum. This kind of nucleation burst produces lots of new particles, even to sizes with a diameter greater than 10 nm. After the nucleation has stopped, the ion concentration reaches rapidly its equilibrium value determined by ion production rate and ion recombination and ion-aerosol attachment coefficients. Depending on conditions, this value can be between few hundreds in dirty air and a few thousands in very clean air with high ion production rate. [39] One interesting phenomenon is that asymmetric nucleation causes imbalance in charge distribution during the nucleation. This is because there are not enough ions to keep the balance. If there is a sign asymmetry, then a clear experimental signature would be a marked divergence of the mobility spectra for positive and negative particles at the onset of a nucleation burst. [40] In case 2 preexisting particle concentration is clean, temperature is 293 K, and ion production rate is 10 ion pairs per cubic centimeter per second. Difference to case one is that the relative humidity is 90% and nucleation is symmetric. Here, Figures 8 10, we have a continuous nucleation, even the nucleation rate slightly decreases at the end of nucleation event. The decay of nucleation rate is also visible in the concentration of small ions. The burst of nucleation onto preexisting ions is also visible. Later on the nucleation rate is limited by ion-production rate. As a result of 4 hours of nucleation, there is a lot of new particles. Because most of the ions nucleate in stead of being attached onto aerosol particles, neutral particles are produced by coagulation. Since the concentration of sulfuric acid is high, we have a situation where equation (8) has zero solutions. For this reason the critical radius is kept constant between about 1000 and 1500 s, see Figure 10. [41] In the third case, Figures 11 13, there are a lot of preexisting particles. Also, temperature and relative humidity are lower than in previous cases, being 273 K and 50%, respectively. Ion production rate is still the same, 10 ion pairs per cubic centimeter per second and nucleation is symmetric. In this case we have continuous nucleation. Also, now the nucleation rate is limited by ion production

12 AAC 5-12 LAAKSO ET AL.: ION-INDUCED NUCLEATION Figure 9. Total particle concentration, number of sulphuric acid molecules and the concentration of negative and positive ions as a function of time. Initial conditions are same as in Figure 8. Nucleation rate 1/cm 3 /s T=293, RH=90 Q=10, Symmetric Clean Time [s] Critical radius [m] Time [s] Figure 10. Nucleation rate and critical radii r 2 from equation (8). Initial conditions are same as in Figures 8 and 9.

13 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC Negative Neutral T=273, RH=50, Q=10 Symmetric, Dirty 10 7 Radius [m] 10 8 Radius [m] Time [h] Time [h] 10 6 Positive 10 6 Total Radius [m] Radius [m] Time [h] dn/dlog(r p ) Time [h] Figure 11. Particle concentration as a function of time, particle radius and particle charge. The initial conditions for this picture have dirty preexisting size distribution, temperature is 273 K, relative humidity is 50% and the ion production rate 10 ion pairs/cc/s. The nucleation is symmetric. For more details, see Figure 5. rate, but because nucleation rate is in this case a bit lower than earlier, there are still some tens of ions left. Because of strong coagulation these particles are not able to grow over 3 nm in diameter, so they are below the DMPS detection limit. This case is consistent with the idea of TSCs [Kulmala et al., 2000b]. [42] We can conclude from these three cases that the particle formation rate is always limited by ion-production rate as it should be according to classical ion-induced nucleation theory. However, the rate of condensation, neutralization of charged particles by ions and coagulation finally determines what is the observable particle formation rate. [43] In Figure 14 the particle size distribution is shown at four separate times, at 0, 100, 1000, and 10,000 s. In this case the ion production rate is 4 ion pairs/cc/s, temperature 273 K and relative humidity 50%. Nucleation type is symmetric. Four separate plots show the concentration of negative, neutral, positive and all particles. At 100 s new nucleated particles are visible at around 1 nm in all plots. The peak is quite sharp because it results from preexisting ions. Since the particles are formed via ion-induced nucleation, the concentration of small neutral particles is smaller than the concentration of charged particles. Later on, at 1000 s, the peak has broadened and moved to larger sizes. At this moment the particles are reaching the sizes that can be observed by DMPS. At 10,000 s, the particles have grown to larger sizes, but the nucleation that is still taking place produces new particles all the time. It is also interesting to note the slight change in charge balance during the nucleation, which is visible for neutral particles around 30 to 100 nm. This is caused by the lack of ions. If this balance exists in the real atmosphere, it can be measured. First experimental results [Mäkelä et al., 2001] suggest nucleation without ions. However, ongoing reanalysis of the data may change this conclusion. [44] In the case of Figure 15 the initial conditions are same as in the case of Figure 14, but nucleation is asymmetric. Compared to symmetric situation, there are no big changes in neutral or total particles. The differences are visible only in the distribution of charged particles. Negative particles peak as in the case of symmetric nucleation, but the change in distribution is visible in positive particles with a long delay. The figure presenting neutral particles shows that fresh negative particles are neutralized very rapidly. There is also a big change in the charged fraction of larger particles, because the timescale of nucleation is much smaller than the

14 AAC 5-14 LAAKSO ET AL.: ION-INDUCED NUCLEATION Figure 12. Total particle concentration, number of sulphuric acid molecules and the concentration of negative and positive ions as a function of time. Initial conditions are same as in Figure 11. Figure 13. Nucleation rate and critical radii r 2 from equation (8). Initial conditions are same as in Figures 11 and 12.

15 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC 5-15 Negative Neutral T=273, RH=50 Q=4, Symmetric Moderate Positive All 0 s s s s Figure 14. Particle concentration as a function of particle radius and charge at times 0 s, 100 s, 1000 s, and s, The initial conditions for this picture have moderate preexisting particle concentration, temperature is 273 K, relative humidity is 50% and the ion production rate 4 ion pairs/cc/s. timescale of ion-aerosol attachment. This prevents charging of larger particles except charging by coagulation. [45] The case of Figure 16 is also shown in more detail in Figures From these figures it is easy to see that even there is ongoing nucleation all the time, newly nucleated particles coagulate with preexisting particles. Thus they are not able to grow further. This result is consistent with the idea of TSCs. [46] Next case, Figure 17, shows nucleation and growth similar to the one observed in locations like Hyytiälä [Mäkelä et al., 1997] and Tahkuse [Hõrrak et al., 1998]. Temperature is in this case 293 K, relative humidity is 50% and ion production rate is 10 ion pairs per cubic centimeter per second. First, nucleation produces lots of new charged particles. Simultaneously, the particles grow via coagulation and condensation. After some time the concentration of sulfuric acid decreases so the nucleation stops. The particle neutralization and charging also starts. As can be seen from this picture, the particles that reach measurable sizes are neutral, even they are a bit overcharged in the very beginning. [47] In addition to results shown here, sensitivity analysis for condensation enhancement factor was done. The enhancement factor used here somewhat overestimates the effect of charge on condensation. For this reason we repeated some model calculations with enhancement factor set half of its actual value or to unity. As pointed out by Yu and Turco [2001], the problem of calculating condensation enhancement factor is both difficult and important. However, in our case the differences between these three cases mentioned above were relative small. If condensation rate is decelerated, the concentration of sulfuric acid rises which rises the nucleation rate. Nucleation rate is, however, limited by ion production rate, so the raise of sulfuric acid concentration accelerates condensation rate. The sensitivity of the system for changes in condensation rate is an interesting topic for further investigations, especially in the case of low relative humidity and high preexisting particle concentration. 4. Conclusions [48] In this paper, we have introduced a new complete model for the investigations of ion-induced nucleation and charged aerosol dynamics. We have also carried out several model runs in order to be able to investigate the properties of ion-induced nucleation and its probability to occur at different temperatures, relative humidities and with different preexisting aerosol particle concentrations. According to

16 AAC 5-16 LAAKSO ET AL.: ION-INDUCED NUCLEATION Negative Neutral T=273, RH=50 Q=4, Asymmetric Moderate Positive All 0 s s s s Figure 15. Particle concentration as a function of particle radius and charge at times 0 s, 100 s, 1000 s, and s, The initial conditions for this picture have moderate preexisting particle concentration, temperature is 273 K, relative humidity is 50% and the ion production rate 4 ion pairs/cc/s. Nucleation is asymmetric. our model simulations, in some preferable conditions (low temperature, low preexisting particle concentration, high relative humidity and high ion production rate) ion-induced nucleation can produce a considerable amount of new particles. This is true both for symmetric and asymmetric nucleation. There are only small differences in final particle concentrations for these two different types of nucleation. [49] The dynamics of the system show that there can be nucleation even when the preexisting particle concentration is high. However, the observation of nucleation is very difficult because the particles coagulate before they have time to grow to observable sizes. [50] Other interesting result is that in certain cases ioninduced nucleation is able to produce similar growth as observed in field measurements. The results also show that if there are some asymmetries in the nucleation rates between positive and negative ions, changes may occur in the charge distribution of larger particles. This may give an opportunity to detect this type of ion-induced nucleation with commonly available instruments like Differential Mobility Particle Spectrometer. Appendix A: Parameters [51] Main constant parameters used in our calculations are presented in Table A1. [52] We have used three different set of preexisting aerosol concentrations in the calculations as defined in Table A2. [53] All parameters are in SI units. Subscripts a and b refer to water and sulfuric acid, respectively. Notation G Gibbs free energy, J n a number of molecules of substance a n b number of molecules of substance b k Boltzmann constant, J/K T temperature, K A ag activity of substance a in gas phase A bg activity of substance b in gas phase A al activity of substance a in liquid phase A bl activity of substance b in liquid phase r radial distance, m r 0 radius of initial ion, m q charge of the particle, C s surface tension N/m 0 vacuum permittivity F/m r relative permittivity m a mass of the molecule of substance a, kg m b mass of the molecule of substance b, kg r density of droplet solution kg/m 3

17 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC 5-17 Negative Neutral T=273, RH=50 Q=10, Symmetric Dirty Positive All 0 s s s s Figure 16. Particle concentration as a function of particle radius and charge at times 0 s, 100 s, 1000 s, and s, The initial conditions for this picture have dirty preexisting particle concentration, temperature is 273 K, relative humidity is 50% and the ion production rate 10 ion pairs/cc/s. v a molecular volume of substance a, m 3 v b molecular volume of substance b, m 3 v volume of virtual monomer m 3 X mole fraction r* critical radius, m S saturation ratio e 0 elementary charge, C r 1 smaller of critical radii in ion-induced nucleation, m r 2 larger of critical radii in ion-induced nucleation, m r 3 critical radius in homogeneous nucleation, m Z Zeldowich nonequilibrium factor n ± concentration of positive or negative ions, 1/m 3 I ± nucleation rate of positive or negative particles, 1/m 3 R av average condensation rate, m 3 /s q angle of nucleation current R aa condensation rate of substance a in nucleation, m 3 /s R bb condensation rate of substance b in nucleation, m 3 /s c a number concentration of substance a, 1/m 3 c b number concentration of substance b, 1/m 3 C cond condensation rate, m 3 /s A condensation enhancement factor N i concentration of the particles in size bin i, 1/m 3 R i radius of the particle of size i transitional correction factor b M K n Knudsen number l b mean free path of sulfuric acid molecule, m a sticking probability D b diffusion coefficient of substance b, m 2 /s m air mass of the air molecule, kg d b diameter of the molecule of substance b, m d air diameter of air molecule, m l N i concentration of particles of size i and charge l, 1/m 3 K ij coagulation coefficient between particles with sizes i and j and charges l and m, 1/m 6 a ij coagulation enhancement factor d ij flux-matching distance, m D ij Diffusion coefficient between particles of size i and j, m 2 /s R ij sum of the radii of particles i and j, m v i thermal velocity of the particle of size i, m/s v ij relative velocity of the particles of sizes i and j, m/s m i mass of the particle of size i, kg b crit critical impact parameter, m f(r) potential, V r m minimum apsidal distance, m f C (r) f VdW (r) potential due to Coulomb force, V Van de Waals-potential, V Hamaker constant, J A H

18 AAC 5-18 LAAKSO ET AL.: ION-INDUCED NUCLEATION Negative Neutral T=293, RH=50 Q=10, Symmetric Clean Positive All 0 s s s s Figure 17. Particle concentration as a function of particle radius and charge at times 0 s, 100 s, 1000 s, and s, The initial conditions for this picture have clean preexisting particle concentration, temperature is 293 K, relative humidity is 50% and the ion production rate 10 ion pairs/cc/s. h ± ion-aerosol attachment coefficient, 1/m 6 /s D ion ion diffusivity, m 2 /s d the radius of limiting sphere, m a ion Fuchs a l ion mean free path of the ion, m r a apsidal distance, m v ion thermal velocity of the ion, m/s f ion (r) potential between particle and ion, V m ion mobility, m 2 /V/s d i, j Dirac delta function nclass number of size classes qclass number of charge classes a rec ion-ion recombination coefficient, 1/m 6 Q ± ion production rate, 1/m 3 /s Q nb sulfuric acid production rate, 1/m 3 /s References Ball, R. T., and J. B. Howard, Electric charge of carbon particles in flames, in Thirteenth International Symposium on Combustion, pp , Combust. Inst., Pittsburgh, Pa., Covert, D., V. Kapustin, P. Quinn, and T. Bates, New particle formation in the marine boundary layer, J. Geophys. Res., 97, 20,581 20,587, Dal Maso, M., M. Kulmala, K. E. J. Lehtinen, J. M. Mäkelä, P. Aalto, and C. D. O Dowd, Condensation and coagulation sinks and formation of nucleation mode particles in coastal and boreal forest boundary layers, J. Geophys. Res., 107, /2001JD001053, Table A1. Main Constant Parameters Used in the Calculations Parameter Mobility Mass, amu Positive ions m 2 /V/s 150 Negative ions m 2 /V/s 90 Value Pressure 1000 hpa Hamaker constant J Recombination coefficient m 3 /s SO /m 3 OH 2 1/m 3 Table A2. Preexisting Particle Concentrations a Name Aitken Mode N tot, 1/cm 3 Accumulation Mode N tot, 1/cm 3 Clean Moderate Dirty a Deviation s in both modes is 1.7 and mean radii of Aitken and accumulation modes are 15 and 50 nm, respectively.

19 LAAKSO ET AL.: ION-INDUCED NUCLEATION AAC 5-19 Fuchs, N., On the stationary charge distribution on aerosol particles in a bipolar ionic atmosphere, Geophys. Pure Appl., 56, , Fuchs, N., The Mechanics of Aerosols, Dover, Mineola, N. Y., Fuchs, N., and A. Sutugin, Highly dispersed aerosol, in Topics in Current Aerosol Research, edited by G. Hidy and J. Brock, pp. 1 60, Pergamon, New York, Hoppel, W. A., and G. M. Frick, Ion-aerosol attachment coefficients and the steady-state charge distribution on aerosols in a bipolar ion environment, Aerosol Sci. Technol., 5, 1 21, Hõrrak, U., Air ion mobility spectrum at a rural area, Ph.D. thesis, Univ. of Tartu, Tartu, Estonia, Hõrrak, U., J. Salm, and H. Tammet, Bursts of intermediate ions in atmospheric air, J. Geophys. Res., 103, 13,909 13,916, Howard, J., B. Wersborg, and G. Williams, Coagulation of carbon particles in premixed flames, paper presented at the 7th Faraday Symposium of the Chemical Society, R. Soc. of Chem., London, Kim, T., M. Adachi, K. Okuyama, and J. Seinfeld, Experimental measurement of competitive ion-induced and binary homogeneous nucleation in SO 2 /H 2 O/N 2 mixtures, Aerosol Sci. Technol., 26, , Kulmala, M., Simulating the formation of acid aerosols, in Acidification in Finland, edited by P. Kauppi, P. Anttila, and K. Kenttämies, pp , Springer-Verlag, New York, Kulmala, M., and A. Laaksonen, Binary nucleation of water-sulphuric acid systems: Comparison of classical theories with different H 2 SO 4 saturation vapour pressures, J. Chem. Phys., 93, , Kulmala, M., and Y. Viisanen, Homogeneous nucleation: reduction of binary nucleation to homomolecular nucleation., J. Aerosol Sci., 22, S97 S100, Kulmala, M., J. M. Mäkelä, and A. Laaksonen, Binary ion induced nucleation: Re-examination of the classical theory, Rep. Ser. Aerosol Sci., 19, 33 37, Kulmala, M., P. Korhonen, L. Laakso, and L. Pirjola, Nucleation in boreal forest boundary layer, Environ. Chem. Phys., 22, 46 53, 2000a. Kulmala, M., L. Pirjola, and J. Mäkelä, Stable sulfate clusters as a source of new atmospheric particles, Nature, 404, 66 69, 2000b. Kulmala, M., et al., Overview of the international project on biogenic aerosol formation an the boreal forest, Tellus, Ser. B, 53, , 2001a. Kulmala, M., M. Dal Maso, J. M. Mäkelä, L. Pirjola, M. Väkevä, P. A. Aalto, P. H. Miikulainen, K. Hämeri, and C. D. O Dowd, On the formation, growth and composition of nucleation mode particles, Tellus, Ser. B, 53, , 2001b. Kusaka, I., Z.-G. Wang, and J. H. Seinfeld, Ion-induced nucleation, II, Polarizable multipolar molecules, J. Chem. Phys., 103, , Laakso, L., J. M. Mäkelä, and M. Kulmala, The characteristic time-scales of condensation and coagulation in ion-induced nucleation, in Nucleation and Atmospheric Aerosols 2000, edited by B. N. Hale and M. Kulmala, AIP Conf. Proc., 534, , Mäkelä, J., et al., Observations of ultrafine aerosol particle formation and growth in boreal forest, Geophys. Res. Lett., 24, , Mäkelä, J., et al., Electrical charging state of fine and ultrafine particles in boreal forest air, J. Aerosol Sci., 32, S149 S150, McGraw, R., and A. Laaksonen, Interfacial curvature free energy, the Kelvin relation and vapor-liquid nucleation rate, J. Chem. Phys., 106, , Mick, H. J., A. Hospital, and P. Roth, Computer simulation of sooth particle coagulation in low pressure flames, J. Aerosol Sci., 22, , O Dowd, C., et al., On the photochemical production of new particles in the coastal boundary layer, Geophys. Res. Lett., 26, , Pirjola, L., Effects of the increased UV-radiation and biogenic VOC emissions on ultrafine sulphate aerosol formation, J. Aerosol Sci., 30, , Pirjola, L., and M. Kulmala, Modelling the formation of H 2 SO 4 -H 2 O particles in rural, urban and marine conditions, Atmos. Res., 46, , Raes, F., and A. Janssens, Ion-induced aerosol formation in a H 2 O-H 2 SO 4 system, I, Extension of the classical theory and search for experimental evidence, J. Aerosol Sci., 16, , Raes, F., and A. Janssens, Ion-induced aerosol formation in a H 2 SO 4 -H 2 O system, II, Numerical calculations and conclusions, J. Aerosol Sci., 17, , Raes, F., A. Janssens, and R. V. Dingenen, The role of ion-induced aerosol formation in the lower atmosphere, J. Aerosol Sci., 17, , Reid, R., J. Prausnitz, and B. Poling, The Properties of Gases and Liquids, McGraw-Hill, New York, Seinfeld, J. H., and S. N. Pandis, Atmospheric Chemistry and Physics, John Wiley, New York, Stauffer, D., Kinetic theory of two-component (heteromolecular) nucleation and condensation, J. Aerosol Sci., 7, 319, Weber, R., J. Marti, P. McMurry, F. Eisele, D. Tanner, and A. Jefferson, Measurements of new particle formation and ultrafine particle growth rates at a clean continental site, J. Geophys. Res., 102, , Weber, R., P. McMurry, R. Mauldin, J. Tanner, F. Eisele, A. Clarke, and V. Kapustin, New particle formation in the remote troposphere: a comparison of observations at various sites, Geophys. Res. Lett., 26, , Wiedensohler, A., E. Lutkemeier, M. Feldpausch, and C. Helsper, Investigation of bipolar charge distribution at various gas conditions, J. Aerosol Sci., 17, , Yu, F., and R. Turco, The formation and evolution of aerosol in stratospheric aircraft plumes: Numerical simulations and comparisons with observations, J. Geophys. Res., 103, 25,915 25,934, Yu, F., and R. Turco, Ultrafine aerosol formation via ion-mediated nucleation, Geophys. Res. Lett., 27, 883, Yu, F., and R. Turco, From molecular clusters to nanoparticles: Role of ambient ionization in tropospheric aerosol formation, J. Geophys. Res., 106, , Yue, G., and L. Chan, Theory of formation of aerosols of volatile binary solutions through the ion-induced nucleation process, J. Colloid Interface Sci., 68, 501, M. Kulmala, L. Laakso, and L. Pirjola, Department of Physical Sciences, University of Helsinki, P.O. Box 64, FIN-00014, Helsinki, Finland. (lauri.laakso@iki.fi) J. M. Mäkelä, Institute of Physics, Tampere University of Technology, P.O. Box 692, FIN-33101, Tampere, Finland.