A criterion for new particle formation in the sulfur-rich Atlanta atmosphere

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110,, doi: /2005jd005901, 2005 A criterion for new particle formation in the sulfur-rich Atlanta atmosphere P. H. McMurry, 1 M. Fink, 1 H. Sakurai, 1 M. R. Stolzenburg, 1 R. L. Mauldin III, 2 J. Smith, 2 F. Eisele, 2 K. Moore, 3 S. Sjostedt, 4 D. Tanner, 4 L. G. Huey, 4 J. B. Nowak, 5,6 E. Edgerton, 7 and D. Voisin 8 Received 19 February 2005; revised 6 May 2005; accepted 7 June 2005; published 4 November [1] A simple dimensionless parameter, L, is shown to determine whether or not new particle formation can occur in the atmosphere on a given day. The criterion accounts for the probability that clusters, formed by nucleation, will coagulate with preexisting particles before they grow to a detectable size. Data acquired in an intensive atmospheric measurement campaign in Atlanta, Georgia, during August 2002 (ANARChE) were used to test the validity of this criterion. Measurements included aerosol size distributions down to 3 nm, properties and composition of freshly nucleated particles, and concentrations of gases including ammonia and sulfuric acid. Nucleation and subsequent growth of particles at this site were often dominated by sulfuric acid. New particle formation was observed when L was less than 1 but not when L was greater than 1. Furthermore, new particle formation was only observed when sulfuric acid concentrations exceeded cm 3. The data suggest that there was a positive association between concentrations of particles produced by nucleation and ammonia, but this was not shown definitively. Ammonia mixing ratios during this study were mostly in the 1 to 10 ppbv range. Citation: McMurry, P. H., et al. (2005), A criterion for new particle formation in the sulfur-rich Atlanta atmosphere, J. Geophys. Res., 110,, doi: /2005jd Introduction [2] Atmospheric measurements carried out over the past decade have shown that new particles are often formed by nucleation from the gas phase. A recent review of the literature identified about 100 journal articles that report observations of nucleation throughout the troposphere [Kulmala et al., 2004]. Particle formation occurs in the continental boundary layer, in polluted urban areas, in industrial plumes that contain sulfur dioxide, in the outflows of convective clouds, and over exposed tidal zones. Nucleation is typically observed in the morning or near midday, suggesting that it is photochemically driven. 1 Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota, USA. 2 Atmospheric Chemistry Division, National Center for Atmospheric Research, Boulder, Colorado, USA. 3 Advanced Study Program, National Center for Atmospheric Research, Boulder, Colorado, USA. 4 School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA. 5 Aeronomy Laboratory, NOAA, Boulder, Colorado, USA. 6 Also at Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, USA. 7 Atmospheric Research and Analysis, Inc., Cary, North Carolina, USA. 8 Laboratoire Chimie et Environnement, Université de Provence, Marseille, France. Copyright 2005 by the American Geophysical Union /05/2005JD Measurements have shown that nucleation events often extend over distances of several hundred kilometers [Kulmala et al., 2001; Stanier et al., 2004]; such events are referred to as regional nucleation events. Measurements in the forests of Finland, in the rural German continental boundary layer and in urban areas including Atlanta, Georgia [Woo et al., 2001], Pittsburgh, Pennsylvania [Stanier et al., 2004] and St. Louis, Missouri [Shi, 2003], show that regional nucleation events occur throughout the year, and are observed on 5% to 40% of the days, depending on season and region. Regional nucleation events typically lead to increases in number concentrations by factors of two to ten, and freshly nucleated particles typically grow at rates of 1 to 20 nm/hour to sizes between 10 and 100 nm during the course of a day [Kulmala et al., 2004]. The widespread occurrence of frequent nucleation events and the rapid growth of nucleated particles suggest that nucleation may play an important role in determining the concentration of cloud condensation nuclei (CCN), and therefore in determining the extent of cloud cover [Pirjola et al., 2004; Laaksonen et al., 2005]. The linkage between nucleation and cloud cover therefore needs to be understood in order to establish reliable global climate models. In its most recent assessment, the Intergovernmental Panel on Climate Change identified the indirect effects of aerosols on radiative forcing, through their role as CCN, as one of the areas with greatest scientific uncertainty [Intergovernmental Panel on Climate Change, 2002]. 1of 10

2 Table 1. Summary of ANARChE Measurements Pertinent to Nucleation Parameter Technique Sampling Interval Measurement Uncertainty Reference Institution SO 2 pulsed fluorescence 5 min 25% NCAR, ARA H 2 SO 4 SICIMS a 7.5 s or 30 s ±40% to ±60% [Eisele and Berresheim, 1992] NCAR NH 3 CIMS a 1 s, 4 s ±20% [Fehsenfeld et al., 2002; Nowak et al., 2002] NOAA, GaTech UMN Particle size distributions: 3 40 nm, nm, mm Nano SMPS, b SMPS, 5 min depends on size and Lasair model 1002, OPC c concentration Nanoparticle volatility and hygroscopicity: 4 10 nm Nanoparticle composition: 6 15 nm BC f aethalometer 5 min ±0.1 mg/m 3 or ±15%, whichever is greater [Wang and Flagan, 1990; Woo et al., 2001] Nano TDMA d 5 min size changes measured [Sakurai et al., 2005] UMN to within 5% TDCIMS e occasional ±50% [Smith et al., 2005] NCAR, UMN a (SI)CIMS: (Select Ion) Chemical Ion Mass Spectrometry. b SMPS: Scanning Mobility Particle Sizer. c OPC: Optical Particle Counter. d Nano TDMA: Nanometer Tandem Differential Mobility Analyzer. e TDCIMS: Thermal Desorption Chemical Ionization Mass Spectrometer. f BC: black carbon. [Hansen et al., 1984] ARA [3] While much has been learned about nucleation over the past decade, it is not yet possible to predict, a priori, rates at which particles are formed and grow, or even to know with certainty which species are involved [Kulmala et al., 2004]. Binary nucleation of sulfuric acid and water [Doyle, 1961; Kulmala et al., 1998] was the first atmospherically relevant process for which a theory was developed, and some atmospheric observations are consistent with theoretical predictions for this process [Clarke et al., 1999; Weber et al., 1999; Clement et al., 2002]. However, it is often found that new particle formation rates are orders of magnitude higher than are predicted by the binary theory, especially when nucleation is observed near ground level [Weber et al., 1996, 1999]. These observations have led researchers to conclude that nucleation may involve a species in addition to sulfuric acid and water [Weber et al., 1997]; a leading candidate for this species is ammonia [Kulmala et al., 2000; Napari et al., 2002b; Birmili et al., 2003]. Evidence has also been reported that ion-induced nucleation of sulfuric acid may play a widespread role in the upper troposphere and lower stratosphere [Lee et al., 2003; Lovejoy et al., 2004], that the oxidation of organic iodine compounds may be responsible for nucleation over exposed surf zones [Jimenez et al., 2003] and that complexes of sulfuric and aromatic acids reduce the energy barrier for nucleation [Zhang et al., 2004]. Species that are responsible for the growth of freshly nucleated particles may be different from those that participate in nucleation. Measurements have shown that condensation of sulfuric acid vapor (and its associated water and ammonia) often accounts for only a fraction of the observed growth [Weber et al., 1997, 1998a; Birmili et al., 2003]. Measurements suggest that organic compounds may be responsible for much of the nanoparticle growth during nucleation events in the boreal forests of Finland [O Dowd et al., 2002]. [4] This paper analyzes data collected during the Aerosol Nucleation and Real Time Characterization Experiment (ANARChE), which took place in the city of Atlanta during August The Jefferson Street sampling site, where these measurements were carried out, is described by Solomon et al. [2003]. In this paper we focus on conditions that lead to new particle formation, and also examine the sensitivity of nucleated nanoparticle concentrations to concentrations of gas phase ammonia. 2. Experiment [5] A summary of parameters measured during ANARChE that are pertinent to this paper is shown in Table 1. Most details of the measurement techniques are discussed in the cited references. It should be pointed out that in this study, an active control system was used to maintain the relative humidities of particles at 40% during measurement of size distributions. The control system made use of a Permapure Model MD S Nafion semipermeable membrane [Woo, 2003]. Properties and composition of the freshly nucleated nanoparticles were measured with the Nano TDMA and the TDCIMS. Results of those measurements are discussed in companion papers [Sakurai et al., 2005; Smith et al., 2005]. Measurements were carried out around the clock in a field sampling laboratory that was installed for the study. 3. Theory [6] Nucleation occurs when stable molecular clusters are formed spontaneously from the gas phase. These clusters may contain a single or multiple species. The current thinking about photochemically driven nucleation in the atmosphere is that stable nuclei contain sulfuric acid and water, or sulfuric acid, water, and ammonia, although this has not been demonstrated definitively and, as was discussed above, alternative hypotheses have been suggested. New particle formation occurs if nucleated particles grow to a size that can be detected. The minimum detectable size for aerosol particles is currently about 3 nm [Stolzenburg and McMurry, 1991]. Some nucleated particles will be lost by coagulation with preexisting particles before they grow to this size. If this loss rate is sufficiently high, new particle formation would not be observed even if nucleation were taking place. The distinction between nucleation and new particle formation was discussed originally by McMurry and Friedlander [1979]. 2of10

3 [7] A simple, limiting criterion for determining whether or not new particle formation will occur in an aerosol that is undergoing nucleation driven by gas phase chemical reactions can be determined by comparing rates at which stable nuclei are lost by coagulation to preexisting particles and grow by condensation. Assuming accommodation coefficients of unity and using kinetic theory, the ratio of these rates, L j, can be expressed as: dn j c dt j jn j loss to preexisting particles 4 L j ¼ dn j ¼ A Fuchs ¼ c ja Fuchs Lf ðþ j dt j loss to size jþ1 b 1j N 1 N j 4b 1j N 1 ð1þ where c j = mean thermal speed of clusters of size j N j = concentration of clusters that contain j molecules (Note that N 1 is the concentration of the condensing vapor) A Fuchs ¼ 4p 3 Z 1 D 2 Kn þ Kn 2 p 1 þ 1:71Kn þ 1:33Kn 2 nd p ddp ð2þ Kn = 2l D p D p D p min b 1j D p min = Cluster Knudsen number = diameter of preexisting particle = diameter above which most surface area is found (10 nm in this study) = collision frequency function of condensing vapor and clusters of size j p 4 ffiffi 2 fðþ¼ j pffi 1=2 ð3þ j 1 þ 1 ð 1 þ j 1=3Þ 2 L L 1 ¼ c 1A Fuchs 4b 11 N 1 The kinetic theory of gases is used to evaluate c j and b 1j [McMurry, 1983]. The Fuchs surface area, A Fuchs [Fuchs and Sutugin, 1971] accounts for the fact that preexisting atmospheric particles have sizes that fall in the transition between free molecular and diffusional cluster transport regimes. The steady state concentration of the condensing vapor can be expressed as: N 1 4R=c 1 A Fuchs where R is the rate of monomer production per volume of gas. In Appendix A we show that the expression for L given by equation (4) is equal to that derived previously [McMurry and Friedlander, 1979; McMurry, 1983]. Other investigators have discussed other criteria for identifying days on which nucleation occurs, and relationships among these approaches are also discussed in Appendix A. [8] Several assumptions or approximations were made in deriving equation (1). It is assumed that if clusters contain more than one species, only one of them (e.g., sulfuric acid) limits condensational growth rates, while others (e.g., water j ð4þ ð5þ vapor and ammonia) rapidly achieve equilibrium when another sulfuric acid is added. Therefore the cluster size, j, is equal to the number of molecules of the rate-limiting species in the cluster, while the cluster mass or volume that is used when calculating c j and b 1j includes the other species as well. Also, the mean free path of clusters, l, depends on cluster size. As an approximation we have assumed that all clusters have the same value of l. We chose l by comparing collision rates of clusters calculated using the above approach with values determined using Fuchs transition regime coagulation expression [Fuchs, 1964] and concluded that a value of l = 0.1 mm provides reasonable estimates (±10%) for overall coagulation rates of clusters ranging in size from one molecule to about 3 nm with preexisting aerosol. [9] The loss ratio in equation (1) decreases with increasing cluster size, indicating that larger clusters of a given size are more likely than smaller ones to grow than to be lost by coagulation with preexisting particles. A rigorous determination of the number of nucleated clusters that will ultimately grow to a detectable size for a given value of L requires a numerical solution of the coupled population balance equations. Such solutions show that for collision-controlled (barrierless) nucleation, new particle formation can occur for L < 1, but decreases rapidly as L increases beyond one [McMurry, 1983; Rao and McMurry, 1989]. This can be understood intuitively by noting that for L = 1, equal numbers of condensing vapor molecules are consumed in producing new particles (j = 2) and condensing on preexisting particles, indicating that new particle formation would be dominant for L <1 and loss of vapor and clusters to preexisting particles would be dominant for L > 1. If a significant nucleation barrier exists, then the concentration of stable nuclei that would be present for a given value of L would decrease. It follows that the likelihood of new particle formation would be even lower in this case. Therefore nucleation should always be insignificant for values of L greater than about one and might be important when L is less than about one. [10] In this analysis we assume that N 1 is the concentration of sulfuric acid vapor molecules, which was measured. We also assume that particle growth rates are limited by sulfuric acid condensation rates, and that growing particles consist of ammonium sulfate. This assumption is consistent with Nano TDMA [Sakurai et al., 2005] and TDCIMS [Smith et al., 2005] measurements, which show that freshly nucleated particles at this site consisted primarily of ammonium and sulfate. (We define particles as freshly nucleated if it is apparent from size distribution data that they have grown during the course of the day from the smallest detectable size (3 nm), or if they are included with a burst of nanoparticles that is well correlated with the impact of a sulfur dioxide plume. Both types of freshly nucleated particles are included in Figure 1, which is discussed below.) It is also consistent with the work of Stolzenburg et al. [2005], who found that growth rates of nucleated sub-15 nm particles are reasonably explained by the condensation of sulfuric acid during the periods investigated. Stolzenburg et al. [2005] also found that growth rates of larger (40 nm) particles exceeded values that could be explained by sulfuric acid condensation during two 3of10

4 Figure 1. Contour plot (a) of aerosol size distributions measured on 23 August 2002 and (b) of the dimensionless criterion for new particle formation, L, and the ternary nucleation rate, J Ternary. Both Figures 1a and 1b include data for the complete 24-hour day. L was calculated from equation (4) using measured values of sulfuric acid (N 1 ) and aerosol size distributions (used to calculate A Fuchs ). J Ternary was calculated using the theory of Napari et al. [2002b]. [12] Similar data are shown in Figure 2 for 27 August, when no evidence for the production of sub-10 nm particles by nucleation was observed. Note that on this day L dropped to 1.0 for a very short period just before 9:00, but subsequently remained above 1.0 for the remainder of the day. Note also that ternary theory predicts that nucleation occurred on this day, but at much lower rates than are predicted for 23 August (Figure 1b). Under such conditions, few new particles would be formed, and those that are would mostly be scavenged by preexisting particles before they grow to a detectable size. [13] The remainder of the discussion focuses on the relationship between the concentration of particles in the 3 to 4 nm diameter range (N 3 to 4 nm ) and other measured variables. These are the smallest particles that could be detected with our instrumentation. By definition, if the formation of detectable particles were occurring, then particles in this size range would be detected. We began by examining data from days during which new particle formation was not observed. Data from a day of this type are shown in Figure 2. On these days we did not observe a significant increase in concentrations of sub-10 nm particle concentrations during the course of the day, nor did we see evidence of nanoparticle growth. However, low concentrations of particles in all size ranges, including 3 to 4 nm, were observed. Unlike particles produced by photochemical nucleation, which are typically observed near midday (Figure 1), these particles were observed throughout the 24 hour day. We are confident that our measurements are valid, because during the August period there were midday growth events, and this could contribute to some of the scatter in the results discussed below. 4. Results and Discussion [11] Figure 1 shows data for 23 August 2002, when a regional nucleation event was superimposed upon periods of intermittent SO 2 plume impacts. The contour plot in Figure 1a shows time of day on the abscissa, particle size on the ordinate, and value of the size distribution function in color. Although the birth of new particles was not observed at the smallest detectable sizes early in the morning, particle concentrations increased during the morning and particles were observed to grow continuously from about 9:00 until 15:00. The high concentrations of 3 to 5 nm particles observed periodically between 10:00 and 13:00 were correlated with elevated levels of SO 2, suggesting that they were associated with a plume containing combustion emissions. Figure 1b shows a time series of L, calculated using measured concentrations of sulfuric acid (N 1 ) and aerosol size distributions. Also shown are calculated ternary nucleation rates [Napari et al., 2002b], based on measured temperature, and water vapor, sulfuric acid and ammonia concentrations. Note that L falls below 1.0 between 9:00 and 15:00, during the period when elevated concentrations of sub-10 nm particles were observed. Note that in this paper all times are Eastern Standard Time. Figure 2. Contour plot of (a) aerosol size distributions measured on 27 August 2002 and (b) of the dimensionless criterion for new particle formation, L, and the ternary nucleation rate, J Ternary. Both Figures 2a and 2b include data for the complete 24-hour day. L was calculated from equation (4) using measured values of sulfuric acid (N 1 ) and aerosol size distributions (used to calculate A Fuchs ). J Ternary was calculated using the theory of Napari et al. [2002b]. 4of10

5 Figure 3. Number concentration of particles with mobility diameters in the 3 to 4 nm range versus black carbon concentrations between 9 a.m. and 3 p.m. on days when photochemical nucleation was not observed min periods when concentrations of 3 to 4 nm particles were measured using two independent instruments. One of these was the scanning Nano SMPS listed in Table 1, and the second was a Nano DMA/PHA-UCPC [Saros et al., 1996; Weber et al., 1998b] system that continuously measured the 3.5 nm size distribution function. Because the latter instrument did not scan through the Nano DMA voltages, as is done with the Nano SMPS, more 3 to 4 nm particles were counted during each 5-min measurement period, and counting statistical uncertainties were much lower than for the Nano SMPS. We found that 88% of the 3 to 4 nm counts measured using the scanning Nano SMPS were within two standard deviations of the values measured using the Nano DMA/PHA-UCPC system, compared to 95% predicted by theory. The small discrepancy between the two instruments is likely due to the fact that the measurements by two instruments are not exactly contemporaneous: the Nano DMA-UCPC sampled continuously at 3.5 nm, while the Nano SMPS scanned over a range of sizes and only measured particles in the 3 to 4 nm range during a fraction of the 5-min sampling period. [14] We hypothesize that the 3 to 4 nm particles that were observed on nonnucleation days are primary particles, possibly vehicular emissions. Figure 3 shows the relationship between N 3to4nm and aethalometer measurements of black carbon (BC) concentrations [Hansen et al., 1984] which originate primarily from vehicles. The solid lines show an approximate upper bound for N 3to4nm versus BC. The relationship between N 3 to 4 nm and BC was similar throughout the 24-hour day on days when photochemical nucleation was not observed. We hypothesize that the increase of N 3 to 4 nm with BC at low BC concentrations reflects their common source, and the variability of N 3to4nm at a given value of BC reflects the varying lifetimes of sampled air parcels. The coagulation lifetime of 3.5 nm particles in Atlanta typically ranges from 10 to 30 min, depending upon the aerosol loading, so significant depletion could occur during transport to the sampling site. We hypothesize that the observed decrease in the upper bound for N 3to4nm for high BC concentrations reflects the rapid depletion of N 3 to 4 nm that occurs when aerosol concentrations are high. In the following analysis we use the results shown in Figure 3 to distinguish between 3 to 4 nm particles that could have been due to vehicular emissions (we refer to these as urban background particles) from those that were probably formed by photochemical nucleation. When N 3 to 4 nm was above the line, we argue that these particles were due to photochemical nucleation. Note that the criterion is not perfect since several points fall above the line. [15] Figure 4 shows N 3to4nm versus average values of L measured during the same 5-min period for all data obtained between 9 a.m. and 3 p.m. during the ANARChE study. The open circles apply to the min measurement periods during which N 3 to 4 nm was above the urban background criterion discussed above, and the crosses apply to the 1344 data points that fell below this criterion. The solid curve shows the expected relationship between steady state N 3 to 4 nm and L if nucleation were collision controlled [McMurry, 1983]. Solutions of the time-dependent population balance equations show that these steady state values of 3 to 4 nm concentrations are achieved after 15 to 200 min under conditions pertinent to these measurements (sulfuric acid production rates of cm 3 s 1 to cm 3 s 1, calculated from equation (5) assuming a Figure 4. Concentration of 3 to 4 nm particles versus the average value of L (equation (1)) measured during the same 5-min period. All data measured between 9 a.m. and 3 p.m. during the ANARChE study are shown. The solid line showing the upper limit prediction of collision-controlled nucleation was obtained using previously published results [McMurry, 1983]. To enable measurements with zero CPC counts (N 3to4nm = 0) to be displayed on the logarithmic plot, they are shown at the bottom (N 3to4nm =10cm 3 ). 5of10

6 Figure 5. Number concentration of particles with mobility diameters between 3 and 4 nm versus ammonia mixing ratios for all ANARChE data measured from 9 a.m. to 3 p.m. that fell above the urban background criterion for data having values of L between 0.18 and 0.4. Standard errors in the best fit parameters and statistical information are provided in Table 2. steady state balance between production and loss.) Note that except for seventeen data points, the collision-controlled theory provides a reasonable upper bound to measured values of N 3to4nm. An examination of the seventeen data points that fall above the collision-controlled limit shows that eight of them occurred on days that on the basis of measured distribution functions of sub 10 nm particles, nucleation probably did not occur. We conclude that those data are likely urban background measurements that fell above the criterion set in Figure 3. Nucleation may have been occurring when the remaining nine data points were measured. There are several factors that may be responsible for pushing these points above the limit, including nonsteady conditions (e.g., insufficient time to establish steady state, or periods when the sampled air mass was temporarily shaded by clouds, which would lead to rapid reductions in [H 2 SO 4 ], but a longer persistence of elevated N 3 to 4 nm ). Also, we assume that growth is entirely due to condensation of sulfuric acid and its associated ammonium or water. It is possible that other species, such as organics, may have contributed to growth on some occasions. In this case, the true value of L would have been smaller than the value plotted on Figure 4 (i.e., the true cluster growth rates would have exceeded the growth rate due to condensation of sulfuric acid alone, which was used in evaluating the denominator of equation (1)). All other measurements at high values of L fall below the urban background criterion, suggesting that they originated from primary emissions and not photochemical nucleation. [16] The results in Figure 4 also show that at a given value of L, values of N 3to4nm vary over several orders of magnitude. Figure 5 shows the dependence of N 3to4nm on ammonia mixing ratios for a relatively narrow range of L values (0.18 < L < 0.4). Although there is considerable scatter, the data suggest that N 3to4nm tends to increase with increasing ammonia mixing ratios. This dependence may help to explain the variability in the dependence of N 3 to 4 nm on L that is observed in Figure 4. Table 2 summarizes observed relationships between N 3to4nm and ammonia for all 9 a.m. to 3 p.m. ANARChE data above the urban background criterion. The last column is the probability of finding the calculated slope if there were no correlation between N 3to4nm and [NH 3 ], on the basis of the two-tailed t-test. According to this statistic, the first (0.18 < L < 0.4) and last (1 < L < 2) slopes are positive at the 95% confidence level. No association was found between N 3to4nm and [NH 3 ] for 0.4 < L < 0.8. For the other ranges of L, there is a weak but suggestive dependence. These observations support the hypothesis that both ammonia and sulfuric acid participate in new particle formation, but the association is not sufficiently strong to show this definitively. The current theory for ternary nucleation [Napari et al., 2002b] suggests that nucleation rates should be independent of ammonia mixing ratios above 0.1 ppbv. During ANARChE, ammonia mixing ratios typically fell in the 1 to 10 ppbv range. If the observed sensitivity is borne out in future studies, the ternary theory would need to be revisited. In any event it appears that the sensitivity of nucleation rates to ammonia does not explain much of the variability of N 3to4nm (L) in Figure 4. This suggests that some other species may have participated in nucleation. [17] Figure 6 shows the relationship between N 3 to 4 nm and sulfuric acid concentrations for all daytime data collected during ANARChE. Figure 6 presents an alternative approach to interpreting our data, along the lines of the arguments made by Clement et al. [2001]. They argue that one might expect to find evidence for nucleation when concentrations of the nucleating vapor (believed to be sulfuric acid in our case) exceed a critical value, but not below that value. As can be seen in Figure 6, we often observed nucleation when sulfuric acid concentrations exceeded cm 3, but not for lower levels, so this might be interpreted as the minimum vapor concentration required for nucleation. Indeed, ternary nucleation theory Table 2. Sensitivity of N 3to4nm on Ammonia Mixing Ratios Range of L Values Count Average [H 2 SO 4 ], Least Squares Fit: Probability That N 3to4nm 10 7 cm 3 N 3to4nm = R 2 Is Not Dependent on NH < L < ± 6.6 Exp(8.28 ± 0.64)*[NH 3 ] 1.17± < L < ± 3.7 Exp(8.49 ± 0.48)*[NH 3 ] 0.19± < L < ± 2.2 Exp(8.89 ± 0.48)*[NH 3 ] 0.09± < L < ± 1.4 Exp(6.24 ± 1.56)*[NH 3 ] 1.93± < L < ± 1.8 Exp(5.85 ± 1.09)*[NH 3 ] 2.32± of10

7 formation of stable molecular embryos, but that other species were required to account for the high subsequent growth rates that were observed [Kulmala et al., 2002]. Our analyses suggest that in Atlanta, nanoparticle growth can often be explained by the condensation of sulfuric acid and its associated ammonia [Stolzenburg et al., 2005], a result that is consistent with our independent observations that freshly nucleated nanoparticles were composed mostly of ammonium sulfate [Sakurai et al., 2005; Smith et al., 2005]. There were times, however, when observed growth rates were too high to be explained by sulfuric acid condensation, and during those times organics may have participated in growth. Unfortunately, we did not obtain measurements of nanoparticle composition during such episodes. Figure 6. Number concentration of particles with mobility diameters between 3 and 4 nm versus sulfuric acid vapor concentration measured during the same 5-min period. All data measured between 9 a.m. and 3 p.m. during the ANARChE study are shown. [Napari et al., 2002a] predicts that at 298 K and with ammonia concentrations of 0.1 ppb, nucleation rates should decrease rapidly as sulfuric acid concentrations drop below cm 3. Figures 4 and 6 provide complementary information regarding factors that influence whether or not new particle formation is observed. [18] In a previous paper we argued that sub-10 nm size distributions measured in Atlanta during nucleation events are consistent with expectations for collision-controlled nucleation [McMurry et al., 2000]. That paper was based on the observed functional dependence of nanoparticle size distributions measured during nucleation events on particle size. Sulfuric acid concentrations were not measured in that study, so it was necessary to make assumptions when calculating L and R. Figure 7 compares a nanoparticle size distribution measured during an ANARChE nucleation event, when sulfuric acid was measured, with predictions of collision-controlled theory [McMurry, 1983]. In this case measurements and theory can be compared assuming only that sulfuric acid is the rate-limiting species for nucleation. Note that theory and experiment show similar functional dependencies on size, but the measurements are a factor of 40 below the theory. In other cases measurements ranged from a factor of 10 to 100 below theory. These results support the conclusion drawn from the results in Figure 4: Collision-controlled theory provides an upper limit to the number of particles produced, but often significantly overpredicts particle production. [19] In a previous study at the coastal site of Mace Head, Ireland, in which both sulfuric acid and ammonia were measured during nucleation events, it was concluded that ternary nucleation may have been responsible for the 5. Conclusions [20] The growth of nucleated particles to a detectable size involves a competition between the coagulation loss of nucleated clusters to preexisting particles and their growth to larger sizes. Measurements carried out during the ANARChE intensive study of nucleation in Atlanta confirm that new particle formation was observed when the dimensionless parameter, L (equation (4)), was smaller than about one but did not occur when L was greater than about one. L is the rate at which the nucleating vapor molecules condense on preexisting particles divided by the rate at which they collide to produce molecular clusters. The observation that L ffi 1 separates days on which new particle formation can occur from those on which it cannot is consistent with theoretical predictions published about 20 years ago. We Figure 7. Comparison of a size distribution measured in Atlanta during a nucleation event on 19 August 2002 at 11:00 with predictions of collision-controlled theory. The observed functional dependence on size was typically consistent with theoretical predictions, but the measurements were smaller in magnitude. 7of10

8 also found that new particle formation was not observed during periods when sulfuric acid concentrations were below cm 3. [21] Our ANARChE measurements also suggest that when new particle formation was observed, the number concentration of particles with mobility diameters between 3 and 4 nm was sensitive to ammonia mixing ratios, which fell in the 1 and 10 ppbv range during most of our study. If valid, this would be a surprising result, since existing theories predict that ternary nucleation rates of sulfuric acid, ammonia and water are independent of ammonia above 0.1 ppbv. Our measurements, however, exhibit considerable scatter and do not show definitively that particle production was sensitive to ammonia. Appendix A: Relationships Among Published Criteria for Occurrence of New Particle Formation [22] Several approaches have been discussed in the literature for determining whether or not new particle formation will occur on a given day. In Appendix A, relationships among these criteria are summarized using common notation. [23] McMurry and Friedlander [1979] derived the parameter, L, that determines whether nucleated particles will grow to a detectable size when condensable vapor is produced by chemical reaction in the presence of an aerosol and when nucleation is occurring at the collision-limited rate. This parameter is: L ¼ g2 A 2 Fuchs Rb 11 ða1þ where g = c 1 /4 and R is the rate at which the condensable vapor is produced by chemical reactions. Assuming that vapor condensation on preexisting particles is the dominant removal mechanism for the condensing vapor, the steady state balance between vapor (monomer) production and loss is: R ¼ c 1 A Fuchs N 1 =4: ða2þ A is the surface area concentration of preexisting particles and s 1 is the surface area of a condensing vapor molecule. Noting that s 1 ffi 4b 11 /c 1, it follows that A/N 1 s 1 ffi L. Therefore, in addition to determining whether or not nucleated particles can grow to a detectable size, as is argued in this paper, L = 1 determines whether or not cluster scavenging can be neglected in the population balance equations used in nucleation theory. [25] Another approach for identifying days on which nucleation occurs was introduced by Clement et al. [2001] and recently used by Birmili et al. [2003]. This approach assumes that the rate at which condensable vapor is produced varies in proportion to the solar radiation intensity, R I rad. Furthermore, the vapor removal rate, R A, defined by Clement et al. [2001] can also be expressed as R A ffi c 1 A Fuchs /4. It follows from equation (A2) that the steady state concentration of the nucleating vapor is N 1 ¼ 4R c 1 A Fuchs I rad R A : ða4þ Clement and coworkers showed that when I rad /R A was plotted versus I rad for data collected in the Finnish boreal forests, days on which nucleation events were observed were cleanly separated from days on which they did not occur. Birmili and coworkers found a similar result for their measurements in Hohenpeissenberg. The conceptual argument behind Clement s model is somewhat different from arguments that led McMurry to the parameter L. Clement assumes that nucleation only occurs when N 1 exceeds the critical value required to overcome the energy barrier and does not explicitly account for the probability that nucleated particles will grow to a detectable size. In contrast, McMurry s approach assumes that nucleation always occurs but that nucleation will lead to new particle formation only if growth is sufficiently fast relative to coagulation loss to the preexisting aerosol. [26] It should also be pointed out here that the condensation sink (CS) introduced by Kulmala et al. [2001] and used by others is related to the other parameters cited above as follows: It follows that equation (A1) can be expressed as: CS ¼ R A ¼ c 1 A Fuchs =4: ða5þ L ¼ c 1A Fuchs 4N 1 b 11 ða3þ which is identical to equation (4). McMurry [1983] reported numerical calculations which showed that new particle production is suppressed when L > 1. This model assumes that the concentration of the nucleating vapor is greatly in excess of its saturation value, and that nucleation occurs at the collision-limited rate. Whether or not new particle production is observed depends upon the probability that growing clusters reach a detectable size before they are scavenged by preexisting particles. [24] McGraw and Marlow [1983] showed that the classical Becker-Döring theory of homogeneous nucleation can be extended to include cluster removal by preexisting particles, and that this loss term becomes significant when the ratio A/N 1 s 1 is greater than 1, where Kerminen and Kulmala [2002] showed that the probability that a critical nucleus formed at rate J(D* p, t) will grow to size D p before it is scavenged by preexisting particles occurs is: P ¼ jd p; t 0 D * ¼ exp g CS0 p ; t GR J nuc! 1 1 D p D * ; ða6þ p where GR is the diameter growth rate of nucleated particles, CS 0 = CS/4pD, and D is vapor diffusivity. We refer the reader to their paper for the definition of g, which was obtained by fitting a function to numerical simulations. Using similar conceptual ideas but starting with the free molecule transport approximation, Weber et al. [1997] showed that the probability that nucleated particles will 8of10

9 grow from size D p1 to D p2 before they are scavenged by preexisting particles is: ( P ¼ exp 1 " #) A Fuchs 48kT 1=2 1 2 GR p 2 1 r D 1=2 p2 D 1=2 p1 ( ffi exp 2 CS " #) GR 6v 1= p D 1=2 p2 D 1=2 p1 ða7þ Using equations (A5) and (4), and assuming that growth rates are determined by rates of sulfuric acid condensation it can be shown that:! CS GR ffi 4 21=6 3 2=3 p 1=6 v 1=3 1 L: ða8þ This relationship could be generalized to account for contributions of species other than sulfuric acid to growth, as was recently done by Kerminen et al. [2004]. With this result, equations (A7) and (A8) can both be expressed in the form: P ffi exp K f D p1 ; D p2 L ða9þ where K is a constant and where L is defined by equation (4) of this paper and previously by McMurry and Friedlander [1979]. [27] Acknowledgments. This research was supported by the Office of Science (BER), U.S. Department of Energy, grants DE-FG-02-98ER62556 and DE-FG-02-05ER NCAR is supported by the National Science Foundation. L. G. 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