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Interaction between SO2 and submicron atm


Atmospheric Research 54 ?2000. 41–57 www.elsevier.comrlocateratmos

Interaction between SO 2 and submicron atmospheric particles
Veli-Matti Kerminen a, ) , Liisa Pirjola b, Michael Boy b, Arkke Eskola c , Kimmo Teinila ¨ a, Lauri Laakso b, Ari Asmi b, Jukka Hienola b, Antti Lauri b, Veera Vainio b, Kari Lehtinen d , Markku Kulmala b
a

Finnish Meteorological Institute, Air Quality Research, Sahaajankatu 20E, Helsinki FIN-00810, Finland b Department of Physics, P.O. Box 9, Uni?ersity of Helsinki, Helsinki FIN-00014, Finland c Department of Chemistry, P.O. Box 55, Uni?ersity of Helsinki, Helsinski FIN-00014, Finland d VTT Energy, Aerosol Technology Group, P.O. Box 1401, VTT FIN-02044, Finland Received 30 August 1999; received in revised form 12 January 2000; accepted 12 January 2000

Abstract In the atmosphere, oxidation of sulfur dioxide ?SO 2 . to sulfate may occur in the gas phase, in cloud or fog droplets, or in the aerosol phase on the surface or inside aerosol particles. While aerosol phase reactions have been studied in the case of supermicron sea-salt and crustal particles, very few investigations regarding submicron particles are available. In this paper, the importance of aerosol phase sulfate production to the dynamics of submicron particle populations was examined. The investigation was based on model simulations and theoretical evaluations regarding potential SO 2 oxidation reactions. None of the relatively well-quantified aqueous phase reactions was rapid enough to make small nuclei grow to cloud condensation nuclei ?CCN. size within the particle lifetime in the lower troposphere. This is consistent with the few observations showing that the smallest atmospheric particles are enriched in organics rather than sulfate. The amount of submicron particulate matter could be enhanced significantly by certain aerosol phase reactions, but this is likely to require a particle population having a pH close to 7. Aerosol phase reactions could partly explain the apparently too low SO 2-to-sulfate conversion rates predicted by several chemical transport models over polluted regions. In addition to the bulk aerosol phase, SO 2-tosulfate conversion might involve physical adsorption of SO 2 or a compound reacting with it by the particle surface, or it could take place in a liquid surface layer that usually covers atmospheric particles. Reactions involving physical adsorption seem to have negligible influence on the

)

Corresponding author. Tel.: q 358-9-1929-5501; fax: q 358-9-1929-5403. E-mail address: veli-matti.kerminen@fmi.fi ?V.-M. Kerminen..

0169-8095r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 8 0 9 5 ? 0 0 . 0 0 0 3 8 - 7

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dynamics of submicron atmospheric particle populations. Aerosol phase reactions worth future investigation are those occurring in particle surface layers and those occurring in cloud interstitial particles. q 2000 Elsevier Science B.V. All rights reserved.
Keywords: Aerosol particles; Heterogeneous reactions; Aerosol dynamics; Sulfur chemistry

1. Introduction Sulfur dioxide ?SO 2 . is perhaps the most important individual precursor compound for secondary particulate matter in the atmosphere. Of the global SO 2 emission flux of 50–100 Tg ?S.ryear into the atmosphere, roughly half is converted to particulate sulfate ?Chin et al., 1996; Restad et al., 1998.. Most of the sulfate is bound to particles smaller than about 1 m m in diameter, constituting a large fraction of dry particulate matter in this size range ?Heintzenberg, 1989; Eldred et al., 1997.. Submicron sulfate aerosol may influence climate by scattering solar radiation and by increasing the number of particles able to act as cloud condensation nuclei ?CCN. ?Chuang et al., 1997.. In addition to these, sulfate is an important acidifying agent and a potential cause of adverse health effects observed in urban areas ?Dockery and Pope, 1994; Rodhe, 1999.. The conversion of SO 2 to particulate sulfate occurs via multiple pathways, including gas phase oxidation to sulfuric acid followed by condensation into the particulate phase, aqueous phase oxidation in cloud or fog droplets, and various reactions on the surfaces or inside aerosol particles. Of these, the production of gaseous sulfuric acid is well quantified and can be modelled accurately in current tropospheric chemistry models. Globally, the most important formation pathway for tropospheric sulfate is thought to be the in-cloud oxidation of SO 2 by either hydrogen peroxide or ozone ?Chin et al., 1996; Restad et al., 1998; Roelofs et al., 1998.. Although the rate coefficients of these reactions are well known, they usually are rather crudely parameterized in tropospheric chemistry models. Reasons for this are the large number of processes involved, such as cloud microphysics, the availability and consumption of the oxidants, and the transport of chemical compounds between the gas phase and the droplets. In principle, in-cloud sulfate production can be modelled accurately if enough computer power to describe the individual processes is available. In the absence of clouds, SO 2 is known to react effectively with both sea-salt and mineral particles. Reactions with sea-salt are important in areas with high sea-salt and low SO 2 concentrations, such as the remote marine boundary layer ?Sievering et al., 1995; Curciullo et al., 1999.. Reactions with mineral particles are capable of influencing sulfur budgets over large spatial scales, downwind from major dust source areas being especially important ?Dentener et al., 1996; Li-Jones and Prospero, 1998; Zhang and Carmichael, 1999.. Reactions associated with these two particle types produce mainly supermicron sulfate, and thereby do not directly influence the submicron particle phase. Compared with supermicron sea-salt or mineral particles, substantially less is known about the atmospheric importance of aerosol phase SO 2 oxidation associated with submicron particles. Laboratory measurements have demonstrated that SO 2 reacts with both solid and wetted particles ?Judeikis et al., 1978; Novakov, 1982; De Santis and Allegrini, 1992; Santachiara et al., 1993., but extrapolation of these results to atmo-

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spheric conditions has proved to be complicated. Some field measurements have reported large SO 2-to-sulfate conversion rates in plumes originating from power plants or urban centres ?Wilson, 1981; McMurry and Wilson, 1983; Bizjak et al., 1988.. The role of aerosol phase reactions in these plumes has remained unclear, since the measured air masses may have interacted with clouds prior to their arrival at the measurement location. Box model simulations suggest that SO 2 oxidation in submicron particles could be significant under some atmospheric conditions ?Middleton et al., 1980; Saxena and Seigneur, 1987; Liang and Jacobson, 1999.. Excluding a few plume models constrained to relatively small spatial scales ?e.g. Eltgroth and Hobbs, 1979; Hudischewsky and Seigneur, 1989., aerosol phase SO 2 oxidation associated with submicron particles has not been incorporated in any chemical transport model. The primary goal in earlier studies concerning aerosol phase SO 2 oxidation has usually been to investigate whether this process might influence the sulfur budget of the system under investigation. In this work, the subject will be examined from a different perspective: the role of aerosol phase SO 2-to-sulfate conversion in the dynamics of submicron particle populations. The investigation is theoretical, with an emphasis placed on two research topics: ?1. growth of nuclei formed in the atmosphere to sizes large enough to act as a CCN, and ?2. enhancement of the amount of submicron particulate matter. The first topic is of special interest in remote locations in which there are practically no sources for primary submicron particles. Enhancement of submicron particulate matter due to sulfate production modifies CCN activities and scattering properties of particles in the accumulation mode ?Hegg et al., 1996., in addition to which it may influence many bulk properties of the aerosol phase such as its acidity, its ability to absorb solar radiation, and its hygroscopicity. The investigation will be performed in two steps. As a first step, we simulate the evolution of a submicron particle population using a box model which includes aerosol dynamics coupled with gas phase chemistry. At this stage, the interaction of SO 2 with the aerosol phase is parameterised by assuming a certain reaction probability between SO 2 and the particles, with no attempt to model the actual reactions responsible for the SO 2-to-sulfate conversion. The purpose of our simulations is to find out the range of SO 2 reaction probabilities needed to make aerosol phase sulfate production important, either to the growth of small nuclei to a CCN size or to the enhancement of the amount of submicron particulate matter. As a second step, the magnitude of the SO 2 reaction probability is evaluated for known aqueous phase oxidation reactions and for physical adsorption. While this evaluation is highly uncertain for some of the reactions, especially in the case of very small particles, we believe that we can obtain valuable insight on whether, and under which conditions, these reactions could be important in the atmosphere. 2. Approach 2.1. Parameterisation for the reaction of SO2 with aerosol particles Basic equations describing the transport of SO 2 to aqueous droplets and its subsequent oxidation have been derived by Schwartz and Freiberg ?1981. and can be found in

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several text books including that of Seinfeld and Pandis ?1998.. These formulas are designed to be used for known aqueous phase reactions occurring in relatively large droplets, being suitable for investigating cloud chemistry or reactions taking place in supermicron particles such as sea-salt. In this work, we investigate submicron particles which may be aqueous or solid, and for which reactions responsible for the SO 2-to-sulfate conversion are not necessarily known. Because of this, we base our approach on that used commonly in laboratory experiments and in many global models for describing interactions between gaseous compounds and aerosol particles. In this approach, the rate coefficient, R i ?m3 sy 1 ., for the reaction of a compound i with a single particle is written as: Ri s 1 4 c i Ag i ,

? 1.

where g i is the so-called reactive uptake coefficient for the compound i , c i ?m sy1 . is its mean molecular speed in the gas phase, and A is the particle surface area 2 ?Ravishankara, 1997.. For spherical particles, A can be replaced with the quantity p d p , where d p is the particle diameter. With the reservation that the particle surface area A is known, the only unknown in Eq. 1 is the reactive uptake coefficient g . For certain compounds and particle types, the value of g has been determined in laboratory experiments, yet it is unclear how representative these values are for conditions encountered in the atmosphere. In reality, the value of g is not a constant but depends on the chemical composition, size, and the phase state of the particle, on the chemical reaction rate, as well as on the transportation of reacting species from the gas phase to a particle and within the particle ?Ravishankara, 1997; Widmann and Davis, 1997.. Experimental data on the SO 2 reactive uptake are restricted to reactions on solid particles at different relative humidities ?Judeikis et al., 1978; Britton and Clarke, 1980.. Because of this, we perform our computer simulations by keeping g SO 2 as a free parameter which may be different for different size particles. The purpose of this study is to find out the magnitude of g SO 2 required to make the reaction of SO 2 with atmospheric particle populations important. The value of g SO 2 for some specific reactions occurring in the atmosphere will then be evaluated in Section 4. 2.2. Description of the model The interaction between SO 2 and submicron aerosol particles is studied using a Lagrangian-based sectional box model AEROFOR ?Pirjola, 1999. which includes gas phase chemistry ?54 species, 107 reactions., binary homogenous nucleation of H 2 O– H 2 SO4 , condensational transport of H 2 SO4 and H 2 O between the gas and the particulate phases, reactive uptake of SO 2 by the particles, coagulation, and dry deposition of particles. The condensational flux of H 2 SO4 onto a particle is proportional to the difference between the vapour pressure of H 2 SO4 distant from the particle ? pv . and at the particle surface ? pva ., where the latter is determined from the Kelvin equation. The saturation vapour pressures for water and sulphuric acid are calculated according to Preining et al.

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?1981. and Ayers et al. ?1980., respectively. Condensation rates are calculated using the continuum regime theory corrected by a transitional correction factor according to Fuchs and Sutugin ?1971. ?see details in Kulmala, 1990; Pirjola and Kulmala, 1998.. The binary diffusion coefficient for the condensing vapour in air is taken from Reid et al. ?1987.. The mass accommodation coefficient of sulfuric acid on particle surfaces is assumed to be equal to unity. To conserve the mass between the gas and aerosol phases, the flux rates of H 2 SO4 and SO 2 are also taken into account in calculating the gas phase H 2 SO4 and SO 2 concentrations. The reactive uptake flux of SO 2 onto the particle is calculated as described in Section 2.1. The Brownian coagulation coefficient between particles of different sizes is calculated according to Fuchs ?1964., and the diffusion coefficient of a particle with the Cunningham correction factor according to Allen and Raabe ?1985.. The model has a sectional representation for the particle size distribution. In the simulations, we will use 27 sections over the particle diameter range 1 nm–2 m m. Each section is considered to have a specified mean dry diameter, such that all particles belonging to a certain section have a fixed number of H 2 SO4 molecules. The time development of the particle number concentration in each section is similar to that in Raes and Janssens ?1986.. The set of stiff differential equations is solved using the NAG library FORTRAN routine D02EJF ?FORTRAN routine D02EJF, 1990..

3. Model calculations The model requires plenty of meteorological and chemical data as an input. These data were taken from measured values representing clear-sky forest conditions in Southern Finland during late spring ?May 7, 1997.. The ambient temperature and relative humidity were from the data recorded in the SMEAR II measurement station ?61.858N, 24.288E. ?Haataja and Vesala, 1997.. During the simulation period, the temperature and relative humidity varied in the ranges 4–158C and 72–36%, respectively. Each simulation started at 6 a.m., after sunrise, and lasted for 12 h. Initial concentrations and emission rates of gaseous species were prescribed in such a way that the modelled concentrations of ozone and NO x were in agreement with the measurements. The ozone concentration varied between 30 and 48 ppb, the NO x level was rather low, about 0.4 ppb, and the natural hydrocarbon concentrations were in the range 0.3–0.4 ppb. The maximum daytime OH concentration was 3.5 = 10 6 cmy3 . The initial SO 2 concentration was set equal to 100 ppt, but the simulations were repeated using also the value of 1 ppb. Two sets of model runs were performed. The initial aerosol size distribution was assumed to have two log normal modes: the nucleation and the accumulation mode in the first set, and the Aitken and the accumulation mode in the second set. The modal parameters ?total particle number concentration, geometric mean diameter, and geometric standard deviation. selected for these modes are given in Table 1. In the case of the Aitken and the accumulation modes, the chosen parameters are good representatives of those observed at the SMEARII station over a 1-year measurement campaign ?Makela ¨ ¨ et

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Table 1 Modal parameters describing the initial particle size distribution For each mode, N is the particle number concentration, d M is the mode mean diameter, and s is the geometric standard deviation of the mode. Mode Nucleation mode Aitken mode Accumulation mode N ?numberrcm3 . 500 1000 200 d M ?nm. 5 40 150

s
1.1 1.45 1.5

al., 2000.. The choice for the nucleation mode parameters is somewhat arbitrary but, as will be shown later, does not affect the conclusions drawn from the simulations. A number of simulations were performed using different values for the SO 2 reactive uptake coefficient, g SO 2 . A summary of the simulation results, including the mean diameter of the nucleation and the Aitken mode after a 12-h simulation, and the corresponding dry mass change of the accumulation mode is given in Table 2. From the simulated final mean diameters of the two modes, we can estimate how large g SO 2 needs to be in order to trigger significant particle growth to produce new CCN in the atmosphere. Values of g SO 2 required for considerable enhancements in the amount of submicron particulate matter can be evaluated from the dry mass change of the accumulation mode.

Table 2 The mean diameter of the nucleation ? d M, Nuc . or the Aitken ? d M,Ait . mode after a 12-h simulation, together with the enhancement of sulfate mass in the accumulation mode ?Mass change. The reactive uptake coefficients of SO 2 with the nucleation, Aitken, and the accumulation modes are denoted by g SO 2 ,Nuc , g SO 2 ,Ait , and g SO 2 ,Acc , respectively. The mean diameter of the nucleation or Aitken mode grown above 80 nm is somewhat uncertain as it tends to mix with the original accumulation mode. SO 2 s 100 ppt SO 2 s 1 ppb Mass change ?%. 3.3 3.4 6.2 20.5 20.5 3.4 16.9 Mass change ?%. 3.2 3.3 6.7 21.7 20.7 9.1 26.4 d M,Nuc ?nm. 29 29 40 79 12 82 90 d M,Ait ?nm. 57 57 66 82 42 87 88 Mass change ?%. 33 33 66 245 240 48 54 Mass change ?%. 32 33 78 255 240 61 67

g SO 2 ,Nuc
0 10y5 10y3 0.01 10y5 0.01 0.1

g SO 2 ,Acc
0 10y 5 10y 3 0.01 0.01 10y5 10y4

d M,Nuc ?nm. 5 8 9 15 7 28 80 d M,Ait ?nm. 43 43 45 48 41 56 77

g SO 2 ,Ait
0 10y5 10y3 0.01 10y5 0.01 0.1

g SO 2 ,Acc
0 10y 5 10y 3 0.01 0.01 10y5 10y4

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Let us first look at the cases in which the mass transport from the gas to the aerosol phase occurs via the condensation of sulfuric acid alone ?g SO 2 is equal to zero.. From Table 2, we can see that without assistance of other condensable trace gases, the growth of nuclei into the Aitken mode can take place only when the ambient SO 2 concentration is relatively high ?) 1 ppb. and simultaneously, the number of accumulation mode particles is very low ?- 100–200 cmy3 .. These kinds of conditions are unlikely to occur frequently in the lower troposphere. The growth of Aitken mode particles by sulfuric acid condensation is very slow. Note that the simulations represent an upper limit for the condensational growth, since the sulfuric acid mass accommodation coefficient has been assumed to be equal to unity. All in all, these results are consistent with earlier model and field studies, which demonstrate that gaseous sulfuric acid is unlikely to dominate the growth of very small particles at concentration levels typically encountered in the lower troposphere ?Kerminen et al., 1997; Weber et al., 1997; Kulmala et al., 1998; O’Dowd et al., 1999.. Particle growth caused by aerosol phase SO 2-to-sulfate conversion remains negligible up to the value of about g SO 2 s 10y5 ?Table 2.. The growth of nucleation mode particles into the Aitken mode requires g SO 2 values of the order 0.001–0.01, depending mainly on the ambient SO 2 concentration. Significant growth of Aitken mode particles requires g SO 2 ) 0.01 for SO 2 concentrations below 1 ppb. In all cases, the growth of nucleation and Aitken mode particles is assisted by the lower reactivity of SO 2 with the accumulation mode ?lower values of g SO 2 ,Acc . due to less rapid consumption of SO 2 from the gas phase. Enhancement of the amount of submicron particulate matter via aerosol phase reactions becomes comparable to that via SO 2 gas phase oxidation when g SO 2 ?in the accumulation mode. reaches a value of about 0.001 ?Table 2.. Smaller value of g SO 2 would be needed during the winter when photochemical production of gaseous sulfuric acid is slower. Globally, the most important sulfate formation pathway is thought to be in-cloud rather than gas phase oxidation of SO 2 , the former being responsible for 70–90% of the overall sulfate production ?Chin et al., 1996; Restad et al., 1998; Roelofs et al., 1998.. Taken together, these things suggest that aerosol phase SO 2-to-sulfate conversion becomes globally important for g SO 2 between about 0.001 and 0.01. At regional scales, even substantially lower values of g SO 2 might be important. Before continuing, it is worth investigating how sensitive our results are to the selected conditions and to the model performance. Since the values of g SO 2 were prescribed in the simulations, it is clear that our conclusions regarding the significance of aerosol phase reactions depend very little on ambient temperature and relative humidity, as well as on gas phase chemistry. The most significant inaccuracies arise from the treatment of aerosol dynamics in the model. To see the effect of size section density on the model performance, we repeated eight simulations using 81 size sections in our model, AEROFOR. Because of weaker numerical diffusion in runs with 81 sections, the final size distributions were narrower than in runs with 27 sections, especially for the nucleation mode ?Fig. 1.. Simulations with 27 sections underestimated the particle number concentration and overestimated the mass transfer to the accumulation mode. These results confirm the recent findings by Pirjola et al. ?1999. who performed a more detailed analysis on the performance of aerosol dynamics in the

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Fig. 1. Particle size distribution after a 12-h simulation when using 27 ?solid line. or 81 ?dashed line. size sections. The value of g SO 2 has been assumed to be 0.001 and the initial SO 2 concentration is equal to 100 ppt. The initial particle size distribution consists of a nucleation and an accumulation mode, with modal parameters taken from Table 1. The mean diameter of the nucleation mode after the simulation is equal to 9.3 nm when using 27 sections and 10.3 nm when using 81 sections.

model. Differences between simulations with 27 and 81 sections were typically below 10% for the total particle number concentrations, below 5% for the change in accumulation mode mass, and below 20% for the mean diameter of the nucleation or the Aitken mode. We may conclude that inaccuracies in the model performance have practically no influence on our order-of-magnitude estimates concerning the required values for reactive uptake coefficient g SO 2 . Another thing that might influence our results is the shape of the initial particle size distribution. A number of simulations were made in which the modal parameters ?total particle number concentration, geometric mean diameter, and geometric standard deviation. were varied by "50% from the values assumed in Table 1. The growth behaviour of the nucleation or the Aitken mode was influenced very little ?- 5–10%. by these changes. The amount of sulfate produced into the accumulation mode was affected more ?up to 50%., primarily because of the relatively large changes in the surface area of this mode with its modal parameters.

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Under some conditions, air masses may travel large distances without interacting with clouds. A few simulations were therefore repeated by extending the simulation time up to 3 days. As expected, increasing the simulation time by a certain factor affects the system by approximately similarly increasing g SO 2 by the same factor. Thus, although larger atmospheric transport times allow lower values of g SO 2 to be significant, our order-of-magnitude estimates concerning the required values of g SO 2 are not considerably affected by the exact air mass travel times. 4. Reactivity of SO 2 with individual particles In Section 3, we outlined the range of values for g SO 2 needed to make the aerosol phase reaction of SO 2 important, either to the growth of very small particles to a CCN size or to the enhancement of the amount of submicron particulate matter. In this section, we analyse in more detail the possible values of g SO 2 under different atmospheric conditions. At first, we investigate reactions that occur inside aqueous particles; after that, reactions taking place at particle surfaces will briefly be discussed. 4.1. Aqueous phase reactions When the particle is aqueous, an analytical approximation for the species’ reactive uptake coefficient, g i , can be derived. Assuming a quasi-steady state and including possible transport limitations in the gas phase, g i can be expressed by the following equation ?Jayne et al., 1992; Widmann and Davis, 1997.: 1 s 1 q 1 q 1

gi

ai
ci d p 4 ci

gdiff
,

greact

,

? 2. ? 3.

gdiff s

8 Dg , i

greact s
qs dp

Hi RT k i D l , i w coth q y 1rq x ,

(

? 4.

k rD . ? 5. 2 i l ,i Here, a i is the species’ mass accommodation coefficient, Hi ?M atmy1 . is its Henry’s law coefficient, k i ?sy1 . is its first-order reaction rate in the liquid phase, Dg, i and D l, i ?m2 sy 1 . are its diffusivity in the gas and liquid phases, respectively, R ?f 0.082 atm My1 Ky 1 . is the ideal gas constant, and T is the temperature. In subsequent calculations, we assume the values of 10y5 and 10y9 m2 sy1 for Dg, i and D l, i , respectively ?Schwartz, 1988.. Expressions for the required Henry’s law coefficients are taken from Seinfeld and Pandis ?1998. and, unless otherwise mentioned, an ambient temperature of 258C is assumed. Fig. 2 illustrates the dependence of g SO 2 on the SO 2 reaction rate in the aqueous phase. In calculations, it has been assumed that k SO 2 is constant, i.e., the species

(

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Fig. 2. The reactive uptake coefficient g SO 2 as a function of the reaction rate k SO 2 for particles of diameter 10 nm ?dashed line. and 100 nm ?solid line.. The SO 2 mass accommodation coefficient has been assumed to be 0.001, 0.01, 0.1 or 1.

participating in SO 2 oxidation are spread steadily throughout the particle. From the figure, we can see that if the reaction is sufficiently slow, g SO 2 is directly proportional to both the reaction rate and the particle diameter. When k SO 2 becomes larger, g SO 2 approaches the SO 2 mass accommodation coefficient a SO 2 . For all values of k SO 2 , mass transport limitations due to SO 2 gas phase diffusion ?term gdiff . are reasonably low and can be neglected. More detailed inspection of Eqs. 2–5 reveals that the value of g SO 2 is influenced by diffusion limitations of SO 2 inside the particle if the reaction rate k SO 2 is very rapid. For a 100-nm particle with a SO 2 equal to unity, the reduction in g SO 2 due to SO 2 aqueous phase diffusion remains below 10% up to the value of k SO 2 of about 10 6 sy1 . The maximum influence caused by SO 2 liquid phase diffusion is seen for reaction rates between about 10 7 and 10 9 sy1 , when the reduction in g SO 2 varies between about 50% and 70%. The corresponding maximum for a 10-nm particle is seen at reaction rates between about 10 8 and 10 9 sy1 , when the reduction in g SO 2 lies in the range 35–40%. The influence of SO 2 aqueous phase diffusion on g SO 2 decreases rapidly with decreasing SO 2 mass accommodation coefficient. The above examples demonstrate that under most conditions, the reactive uptake of SO 2 in submicron particles is governed by either the SO 2 reaction rate or its mass accommodation coefficient. This is contrary to cloud or fog droplets, for which various mass transport limitations may be quite significant ?Schwartz, 1988.. Neglecting both SO 2 gas and liquid phases diffusion ?gdiff 4 1, q < 1., and recalculating Eqs. 2–5, we obtain: 1 s 1 q 3 cSO 2 2 d p HSO 2 RTk SO 2 .

g SO 2

a SO 2

? 6.

This is an appropriate formula for g SO 2 in practical applications. Measured values of a SO 2 are around 0.1 ?Gardner et al., 1987; Worsnop et al., 1989; Ponche et al., 1993.. If

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this holds for atmospheric particles, the term 1ra SO 2 in Eq. 6 can usually be neglected, and the rate constant given by Eq. 1 takes the following very simple form: R SO 2 s 1 6
3 p dp HSO 2 RTk SO 2 .

? 7.

Eq. 7 can be generalized for cases in which a particle contains an insoluble core of 3 3 3. diameter d 0 by replacing the term d p with the term ? d p y d0 . y 2y In the aqueous phase, SO 2 exists as SO 2 P H 2 O, HSO 3 and SO 3 , each of which may react with an oxidant X to produce sulfate. When this is taken into account, k SO 2 may be written as: k SO 2 s k 0 q k 1 K1 q k2 K1 K2 = wXx ,

wH x
q

w Hq x 2

? 8.

where wXx is the concentration of the oxidant in the solution, K 1 and K 2 are the first and second equilibrium dissociation constants for SO 2 , and k 0 , k 1 and k 2 ?My1 sy 1 . are the 2y reaction rates of X with SO 2 P H 2 O, HSOy 3 and SO 3 , respectively. The values of k SO 2 for three reasonably well-quantified SO 2 oxidation reactions have been calculated in Table 3. Combining the data in Tables 2 and 3 and in Fig. 2, we can immediately see that the aerosol phase oxidation of SO 2 by H 2 O 2 or NO 2 can be neglected when studying the time evolution of a submicron particle population in the atmosphere. The same holds for O 3 oxidation in systems with particle pH below about 6. If the particle pH is close to 7, the reactive uptake coefficient of SO 2 caused by O 3 oxidation may reach values of the order 0.001 or larger. Reaction probabilities of this magnitude are large enough to produce significant amounts of submicron particulate matter, yet too low to make small nuclei grow to CCN size. The reaction rates applied in the above calculations are for dilute solutions, being thereby more accurate for cloud droplets than for aerosol particles. Lagrange et al. ?1994. studied SO 2 oxidation by O 3 in concentrated solutions supported by various electrolytes, and found a significant increase in the oxidation rate with the increasing ionic strength of the solution. The influence of ozone on aerosol phase sulfate production might thus be somewhat greater than what can be estimated from the data in Table 3. The oxidation of SO 2 by H 2 O 2 may be enhanced or suppressed in concentrated

Table 3 The value of k SO 2 for the reaction of SO 2 with H 2 O 2 , NO 2 , and O 3 at 298 K and for particles of different pH The rate constants are taken from Seinfeld and Pandis ?1998.. Oxidant H 2 O2 NO 2 O3 Concentration of the oxidant ?ppb. 0.1–1 0.1–10 30–150 pH s 5 7–70 0.0002–0.02 4–20 k SO 2 ?sy1 . pH s 6 7–70 R 0.03–3 400–2000 pH s 7 7–70 R 0.4–40 0.4–2=10 5

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solutions, depending on the nature and ionic strength of the solution ?Lagrange et al., 1993, 1996.. Despite these uncertainties, the oxidation of SO 2 by H 2 O 2 remains too slow to make this route important for aerosol phase SO 2-to-sulfate conversion. Liang and Jacobson ?1999. investigated aqueous phase oxidation of SO 2 by OH, CH 3 OOH, H 2 O 2 , and O 3 over a wide range of liquid water contents and pH values. Compared with H 2 O 2 , the influence of CH 3 OOH remained negligible under all conditions simulated. Oxidation of SO 2 by OH could exceed that by H 2 O 2 , but only under very specific conditions not likely to be encountered in the absence of clouds. We may conclude that neither OH nor CH 3 OOH is important for aerosol phase SO 2-to-sulfate conversion in the atmosphere. Trace metals, especially Fe?III. and Mn?II., are important catalysts for the oxidation of SO 2 by O 2 in aqueous solutions ?Seinfeld and Pandis, 1998.. Evaluating the importance of these reactions under atmospheric conditions is very difficult. Reasons for this are the complicated equilibrium behaviour of iron between its different forms, the apparent synergism between Fe?III. and Mn?II. in the reaction chain, as well as the dependence of the oxidation rate on the ionic strength of the solution and the amount of organics and sulfate present in it ?Martin and Good, 1991; Martin et al., 1991; Grgic ? et al., 1992.. Many of these phenomena are emphasized in concentrated solutions typical for aerosol particles. By using the reaction rates measured for more dilute systems, a very rough estimate for k SO 2 due to trace-metal-catalysed SO 2 oxidation in aerosol particles can be obtained. The values of k SO 2 , based on the reaction rates reported in the references above, remain quite low for acidic particles. However, if the particle pH is close to 7, trace-metal-catalysed SO 2 oxidation might become rapid enough to enhance the amount of submicron particulate matter. The presence of trace metals has been observed to have no effect on the oxidation of SO 2 by O 3 ; oxidation by H 2 O 2 seems to be enhanced slightly by the presence of F?II. ?Lagrange et al., 1993; 1994.. Other compounds that may influence aqueous phase SO 2 oxidation are soot and various radicals ?Grgic ? et al., 1993; Seinfeld and Pandis, 1998.. The reaction chains involving these compounds are not well quantified, so in the present work, no attempt to evaluate their importance to aerosol phase SO 2-to-sulfate conversion will be made. The above discussion demonstrates that the direct reaction of SO 2 with aqueous submicron particles is unlikely to make small nuclei grow to CCN size in the troposphere. Enhancement of the amount of submicron particulate matter by aerosol phase sulfate production could be important, but most likely requires that the submicron aerosol phase have pH close to 7 or above. These kinds of conditions occur most probably in masses exposed to ammonia emissions and in plumes containing relatively freshly emitted particles. Aged air masses encountered at remote locations are unlikely to be affected significantly by sulfate production in aqueous aerosol particles. 4.2. Surface reactions In addition to aqueous phase reactions, the oxidation of SO 2 to sulfate could occur via surface reactions. If the particle is solid, which may be the case for fresh combustion particles, the oxidation reaction requires physical adsorption of either SO 2 or the compound reacting with it. The importance of this oxidation pathway can be estimated

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by calculating the number of molecules of species i adsorbed on the particle surface, Nads, i , which is given by: Nads , i s bit ,

? 9. ? 10 .

t s t 0 exp w QrRT x .

Here, bi ?molecules sy1 . is the impinging rate of species i on the particle surface, Q ?J moly1 . is the heat of adsorption, and t is the average time of stay for a molecule on the particle surface ?Adamson, 1982.. The value of t 0 is usually of the order 10y1 2 –10y1 3 s. The term Q can be estimated in practise by using the latent heat of condensation ?Lazaridis et al., 1991.. In the present study, we have evaluated t and Nads for SO 2 , as well as for NH 3 , O 3 , H 2 O 2 , and O 2 which are good candidates for species reacting with SO 2 on the particle surface. Typical values of t are of the order t 0 , resulting in Nads less than one molecule per particle. This can be compared with the number of molecules required to form a monolayer around a particle, which is about 80 for a 5-nm particle, 5000 for a 40-nm particle, and about 70,000 for a 150-nm particle. We may conclude that SO 2-to-sulfate conversion initiated by reactions involving the species mentioned above, and having physical adsorption as a starting point, is unlikely to be significant in the troposphere. This is consistent with laboratory measurements demonstrating that g SO 2 is typically in the range 10y8 –10y3 for the reaction of SO 2 with various types of solid particles ?Judeikis et al., 1978; Britton and Clarke, 1980.. In the ambient atmosphere, most particles are either totally aqueous or covered by a liquid layer consisting of water, dissolved inorganic compounds, and possibly some organic material. The liquid surface layer surrounding the particles provides another medium for SO 2-to-sulfate conversion. The potential importance of these layers to SO 2 oxidation has been demonstrated by Judeikis et al. ?1978. and Novakov ?1982. in the case of combustion particles, and by Benner et al. ?1992. in the case of particles exposed to both SO 2 and ammonia. Since a large fraction of dissolved SO 2 and NH 3 is expected to be found on the particle surface layer, especially if particles are smaller than 100 nm in diameter ?Jayne et al., 1990; Shi et al., 1999., surface reactions involving SO 2 are worth keeping in mind when exploring heterogeneous SO 2-to-sulfate conversion.

5. Summary and conclusions Atmospheric oxidation of SO 2 may occur in the gas phase, in cloud or fog droplets, or in the aerosol phase on the surface or inside non-activated aerosol particles. In this work, aerosol phase sulfate production was investigated in order to shed light on whether and under which conditions it could influence either ?1. the growth of small nuclei formed in the atmosphere to CCN size, or ?2. the enhancement of the amount of submicron particulate matter. At first, the time evolution of a submicron particle population was simulated using a zero-dimensional model AEROFOR, in which aerosol dynamics is coupled with a detailed mechanism for gas phase chemistry. At this stage, aerosol phase sulfate production was described using a reactive uptake coefficient, g SO 2 ,

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for the oxidation of SO 2 to particulate sulfate. The value of g SO 2 was prescribed in the simulations. After finding out the range of values of g SO 2 needed to make aerosol phase sulfate production significant for the evolution of a submicron particle population, known relations between g SO 2 and the actual reaction rate were applied to evaluate which kind of oxidation reactions could be important under different atmospheric conditions. Model simulations demonstrated that the growth of nuclei to CCN size by aerosol phase sulfate production requires g SO 2 of the order 0.001–0.01, depending mainly on the ambient SO 2 concentration. Significant enhancement of submicron particulate matter requires somewhat lower g SO 2 of the order 10y4 –10y3 . Globally, aerosol phase sulfate production would become important if g SO 2 reached values greater than about 0.001. The values of g SO 2 , estimated for well-known reactions occurring in the bulk aqueous phase, are too low to make small nuclei grow into CCN size within the particle lifetime in the lower troposphere. Atmospheric CCN production via aerosol phase sulfate production seems therefore unlikely. Contrary to this, certain SO 2 oxidation reactions, such as those initiated by dissolved ozone or trace metals, could significantly enhance the amount of submicron matter if the particles have pH close to 7 or above. In addition to the bulk aerosol phase, oxidation of SO 2 may occur on particle surfaces. The reaction might involve physical adsorption by the particle surface, or it could take place in a liquid layer that usually covers the particle. We demonstrated that SO 2 oxidation via the physical adsorption of SO 2 ?and of NH 3 , O 3 , H 2 O 2 , or O 2 . by solid particles is likely to be negligible. Reactions occurring on the liquid surface layer usually surrounding atmospheric particles have the potential to enhance SO 2-to-sulfate conversion compared with the bulk liquid phase. Atmospheric importance of these yet poorly known surface reactions is worth exploring in future studies. Direct observations of the nuclei growth to sizes between about 50 and 100 nm in diameter are few and restricted mainly to forested areas ?Kavouras et al., 1998; Kulmala et al., 1998; Leaitch et al. 1999.. In these studies, no connection between particle growth and sulfur pollution could be found. Chemical measurements of atmospheric aerosol samples indicate that particles smaller than some 0.1 m m in diameter are enriched in organics rather than sulfate ?Novakov and Penner, 1993; Rivera-Carpio et al., 1996; Hegg and Kaufman, 1998.. Together, these findings are consistent with our prediction that the growth of small nuclei to CCN size is unlikely to be affected significantly by aerosol phase sulfate production. Conditions favouring the overall enhancement of submicron particulate matter by aerosol phase sulfate production occur most likely in air masses exposed to ammonia or in air containing freshly emitted combustion particles. Aerosol phase reactions might partly explain the apparently too low SO 2-to-sulfate conversion predicted by several chemical transport models over polluted regions ?Roelofs et al., 1998; Rodhe, 1999.. Before drawing this conclusion, however, it must be kept in mind that discrepancies between observed and predicted sulfate concentrations may also be due to an improper treatment of cloud processes in current chemical transport models ?McHenry and Dennis, 1994.. A subgroup of particles for which aerosol phase SO 2-to-sulfate conversion is also favoured is hygroscopic cloud interstitial particles. Having relatively large liquid–water content and frequently high pH, these particles could accumulate signifi-

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cant amounts of sulfate during a cloud event, especially if a sufficient amount of gaseous ammonia is present. While unlikely to be important for the nuclei growth or the overall production of submicron particulate matter, aerosol phase reactions occurring in cloud interstitial particles could provide a link between sub-CCN-sized Aitken mode particles and particles that are able to act as CCN in the following cloud cycles. References
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