Environ. Sci. Technol. 2007, 41, 6046-6051
r-Pinene Oxidation in the Presence of Seed Aerosol: Estimates of Nucleation Rates, Growth Rates, and Yield B A R T V E R H E G G E N , †,‡ M I C H A E L M O Z U R K E W I C H , * ,§ PETER CAFFREY,| GLENDON FRICK,| WILLIAM HOPPEL,| AND WILLIAM SULLIVAN⊥ Institute for Atmospheric and Climate Science, ETH Zu ¨ rich, 8092 Zu ¨ rich, Switzerland, Laboratory for Atmospheric Chemistry, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland, Centre for Atmospheric Chemistry and Department of Chemistry, York University, Toronto, Ontario M3J 1P3, Canada, Naval Research Laboratory, Washington, DC 20375, and Calspan, University of Buffalo Research Centre, Buffalo, New York 14225
A recently developed inverse-modeling procedure has been applied to a case study of particle nucleation and growth following R-pinene and SO2 oxidation in a smog chamber. With the use of only the measured aerosol size distributions as input, the condensational growth rate is obtained by regression analysis of the general dynamic equation, taking into account coagulation and wall losses. The growth rate provides an indirect measure of the concentration of the condensing species, offset by their vapor pressures. Assuming a particle density of 1.0 g cm-3, an aerosol yield of 7 ( 1% is obtained for an initial R-pinene concentration of 14 ppbv and a final organic aerosol mass of 4 µg m3. Using the estimated vapor concentration, we show that the time-dependence of the yield is at least partly due to the time needed for condensation. Such a kinetic limitation to secondary organic aerosol formation may have implications for our understanding of gasparticle partitioning. The measured size distributions are also used to determine the empirical nucleation rate; it appears to be enhanced by the presence of organics.
1. Introduction Emissions of biogenic volatile organic compounds (VOCs) exceed anthropogenic VOC emissions 5 to 10-fold (1, 2). An inaccurately known fraction of the VOC photo-oxidation products partitions to the aerosol phase; some of the leastvolatile products may contribute to the nucleation of new aerosol particles. Both of these pathways contribute to the formation of secondary organic aerosol (SOA), which contributes significantly to the total aerosol mass. By increasing the particle size, SOA contributes to the light scattering and absorption of the atmospheric aerosol; this is the direct effect * Corresponding author phone: 416.736.5896; e-mail: mozurkew@ yorku.ca. † Institute for Atmospheric and Climate Science. ‡ Paul Scherrer Institut. § York University. | Naval Research Laboratory. ⊥ Calspan, University of Buffalo Research Center. 6046
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of the aerosol on climate (3). The increase in particle size also improves their ability to act as cloud condensation nuclei, thereby contributing to the indirect effect of particles on climate (4). Ambient measurements in forested regions have shown that biogenic VOCs contribute to the nucleation and/ or growth of ultrafine particles (5-10). R-Pinene is one of the most important biogenic VOCs in the atmosphere, and its oxidation products are known to significantly contribute to the aerosol mass loading (11). Knowledge of the biogenic component of SOA is crucial in evaluating the anthropogenic contribution to the aerosol loading and, thus, the associated climate forcing and health effects. Likewise, the gas-to-particle conversion of semivolatile oxidation products needs to be understood to quantify the formation of SOA in model simulations (2). Many chamber measurements have been performed to quantify the aerosol formation potential (yield) of different VOCs, most notably of terpenes (biogenic) and aromatic compounds (anthropogenic). Due to semivolatile partitioning effects, the aerosol yield, Yaerosol ) ∆Maerosol/∆VOC, increases with increasing organic aerosol mass. This trend is often parametrized using the two-product-yield method (12)
Y ) Maerosol
∑ i
(
aiKi
1 + Ki Maerosol
)
(1)
where ai is the fraction of product i formed from reaction of the precursor hydrocarbon, Ki is its partitioning coefficient (units m3 µg-1), and Maerosol is the organic aerosol mass concentration. Equation 1 is usually applied to final-yield values from different experiments, when the hydrocarbon has been reacted away and particle growth has stopped (12-16). It has also been used to describe the change in yield with time during a single experiment for hydrocarbons whose first-generation products condense to the aerosol phase (14, 17, 18). For these compounds, the amount of condensable vapor produced is proportional to the amount of parent hydrocarbon reacted at any time during the experiment, since no time lag is introduced by the formation of intermediates. This use of eq 1 implicitly assumes that the increase of the yield with time, as typically observed in chamber experiments, is due to a shift in gas-particle partitioning caused by the increase in organic particle mass. However, gas-to-particle conversion may take a finite amount of time; the resulting time lag between the condensable vapor produced and the accumulated aerosol mass contributes to the time-dependence of the yield. This is especially likely at the start of nucleation, when the particle surface area, acting as a sink for the condensable vapor, is extremely small, since these experiments are usually conducted in the absence of seed aerosol. While the source of vapor (by oxidation of the parent hydrocarbon) is larger than its sinks (condensation and wall loss), it becomes supersaturated and nucleates to form new particles, which subsequently grow by condensation, thereby increasing the sink and lowering its concentration. Another factor that contributes to observed yields increasing with time is that nucleated particles are initially too small to be detected by current instrumentation and growth into the measured size range takes time. Here, we report on measurements of particle nucleation and growth following R-pinene and SO2 oxidation, conducted in Calspan’s 590 m3 environmental chamber in Buffalo, U.S.A. A key quantity in our analysis is the particle growth rate, which is proportional to the concentration of the condensing 10.1021/es070245c CCC: $37.00
2007 American Chemical Society Published on Web 08/08/2007
species above saturation. Combining this with a simple chemical box model allows for a novel analysis of the partitioning behavior, including the estimation of the aerosol yield. Usually, the growth rate is estimated from the rate of change of the geometric mean diameter (9, 19) or from the evolution of the maximum particle number in the size distributions by fitting the trajectory of highest particle concentration in a contour-plot of diameter versus time (5, 20, 21). Thus, only the maximum in the particle size distribution is used, and the estimated growth rate is averaged over relatively long time scales, thereby masking variations in the growth rate. We determine the condensational growth rate using the inverse-modeling procedure particle growth and nucleation PARGAN (22). This procedure is based on fitting the general dynamic equation (GDE) to the observed change in the aerosol size distribution and provides an accurate and highly time-resolved estimate of the growth rate, taking into account wall losses and coagulation.
2. Experimental Section and Model Description A detailed description of the Calspan environmental chamber and its instrumentation is given by Hoppel et al. (23). The chamber has a total volume of 590 m3 and a surface-tovolume ratio of 0.67 m-1. It has a large mixing fan, and the interior is Teflon coated. A filtration system lowers measured gas-phase and aerosol concentrations to below detectable levels by overnight filtration. Air removed from the chamber for sampling was replaced through absolute aerosol and charcoal filters. The aerosol size distributions from 8.8 to 800 nm diameter were measured using a Naval Research Laboratory differential mobility analyzer (DMA) and MetOne 1100 condensation particle counter (CPC) in scanning mode. The filtered and recirculated sheath air of the DMA was dried, and the aerosol sample was removed from the chamber through a diffusion dryer. A complete scan was measured every 288 s. The measured size distributions were corrected for particle losses in the sample lines and for reduced CPC counting efficiency at small particle sizes prior to data analysis. R-Pinene was measured using GC/MS in conjunction with thermal desorption. The system consisted of a Hewlett-Packard model 5890 Series II+ with a Discovery 2 quadrupole ion trap MS from Teledyne Electronic Technologies, Inc., and a Dynatherm ACEM 900 single-tube thermal desorption unit. SO2 and O3 were monitored using a TECO model 43S and a Dasibi model 1008, respectively. Measured R-pinene and O3 concentrations were corrected for an offset in the zero reading. The inverse-modeling procedure PARGAN is used to determine the particle nucleation and growth rates from the measured aerosol size distributions. It has been described in detail by Verheggen and Mozurkewich (22); more information is also given in the Supporting Information. In PARGAN, the kinetic-limit growth rate due to condensation is determined by nonlinear regression analysis of the GDE to fit the measured change of the aerosol size distribution in time. The size-dependence of the growth rate due to diffusion limitation is taken into account. The GDE describes the evolution of the size distribution due to wall losses, coagulation, and condensation. Knowing the growth rate as a function of time enables the evaluation of the time of nucleation of measured particles of a certain size, assuming that the diameter of the critical cluster is1 nm (24, 25). The nucleation rate is determined by integrating the loss processes (coagulation, wall losses) that have occurred between time of formation and time of measurement.
3. Measurements and Discussion An ozonolysis experiment in the absence of light, conducted on 12 Nov, 1998, is analyzed here in detail. An ammonium
FIGURE 1. Measured size distributions on 12 Nov, 1998. O3 injections took place at 9:50 and 13:33. The chamber was filtered from 12:28 to 13:06 to reduce concentrations. sulfate solution was nebulized at 9:00 to create seed aerosol (10 000 particles cm-3, surface area 270 µm2 cm-3), after which 15 ppbv of R-pinene and 100 ppbv of O3 were injected at 9:27 and 9:50, respectively, at a constant relative humidity of 50% and a temperature of 24 °C. The pre-existing aerosol was observed to grow in size by condensation, but no significant nucleation occurred. The chamber was filtered from 12:28 to 13:06; this decreased the aerosol concentration to 450 particles cm-3 with a total surface area of 22 µm2 cm-3. Then 15 ppbv R-pinene, 2.5 ppbv SO2, and 100 ppbv O3 were injected into the chamber at 13:11, 13:26, and 13:33, respectively. The relative humidity was gradually increased to 85%, but since particles originating from the oxidation of R-pinene are only very slightly hygroscopic (26), we assume that the uptake of water vapor is negligible compared with the uptake of organic material. A large nucleation event was observed, and both the nucleation mode and the pre-existing mode grew in size. Figure 1 shows the evolution of the measured aerosol size distributions. 3.1. Kinetics of Gas-Phase Reactants. As soon as O3 is injected into the chamber, R-pinene and SO2 start becoming oxidized. The oxidation of R-pinene leads to many different compounds, some of which, such as pinic acid or norpinic acid, have low enough vapor pressures to condense to the particle phase (27). Since it is likely a group of products that condense onto the particle phase and not all are known, the group of condensable oxidation products of R-pinene is called “pinox” in the following. To determine the mixing ratios of gas-phase and condensable species, the chemical kinetics are simulated using the following rate equations, where RP is R-pinene
d[O3] ) -kwall,O3[O3] - kO3+RP[O3][RP] dt
(2)
d[RP] ) -kO3+RPβ[O3][RP] dt
(3)
d[pinox] ) ψkO3+RPβ[O3][RP] - kwall,pinox[pinox] dt kcond,pinox[pinox] (4) d[H2SO4] ) kOH+SO2[OH][SO2] - kwall,H2SO4[H2SO4] dt kcond,H2SO4[H2SO4] (5) Here, kwall,x is the first-order rate constant for the wall loss of species x. For H2SO4 and pinox, kwall was estimated to be 4.0 h-1 by using the same dependence as that found for aerosol particles (22), with a diffusion coefficient of 0.1 cm2 s-1 (28). The value of kwall,O3 was measured to be 0.17 h-1 (23); VOL. 41, NO. 17, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Mixing ratio of gases injected into the chamber. Calculated curves are based on the chemical kinetics scheme; the fitted curve for SO2 is based on an exponential decay. since this is a reaction on the walls, it is reasonable that it is slower than the mass transport limit. R-Pinene was not observed to be lost to the walls. kcond,x is the (time-dependent) pseudo-first-order loss rate of species x due to condensation onto the particles (i.e., the inverse lifetime, also called the condensation sink), calculated from the measured aerosol size distributions and the Fuchs-Sutugin equation (22, 29). The resulting values are discussed in section 3.3. The secondorder rate constant for the reaction of species x + y is given by kx+y; we use kO3+RP ) 8.7 × 10-17 cm-3 s-1 (30) and kOH+SO2 ) 8.9 × 10-13 cm-3 s-1 (31). ψ is the molar yield of pinox from R-pinene oxidation, obtained from fitting [pinox] to the particle growth rate (see section 3.2). β is the number of R-pinene molecules consumed per ozone molecule; this is greater than unity due to production of and subsequent oxidation by OH. The steady-state concentration of OH, used in eq 5, is given by
kO3+RPφ[O3][RP]
[OH] )
kOH+RP[RP] +
∑k
(6)
OH+X[X]
where X is any species present, other than R-pinene, that reacts with OH (e.g., R-pinene oxidation products or SO2). The number of R-pinene molecules oxidized by OH, per O3 + R-pinene reaction, (i.e., β - 1) equals the OH yield, φ, times the fraction of OH that reacts with R-pinene
kOH+RP[RP] kOH+RP[RP] +
∑
(7)
kOH+X[X]
X
Substituting eq 7 into eq 6 gives
[OH] ) (β - 1)
kO3+RP[O3] kOH+RP
(8)
where kOH+RP ) 5.4 × 10-11 cm-3 s-1 (30). Equation 8 shows that the OH concentration can be deduced without knowing the loss rate of OH to species other than R-pinene. Fitting the measured decay of O3 (eq 2) and R-pinene (eq 3) resulted in a value of 1.6 for β. This agrees with the constraint that β - 1 e φ, since several studies found the OH yield for this reaction to be between 0.68 and 0.91 (32). The mixing ratios of the gas-phase species are shown in Figure 2. The SO2 measurements were fit to an exponential decay with a decay rate of 1.3 h-1; this is almost entirely due to wall loss. The O3 and R-pinene concentrations were 6048
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calculated using eqs 2 and 3, respectively, with the initial concentrations fit to the measurements. 3.2. Particle Growth Rate and Yield. Figure 3 shows the radius growth rate in the kinetic limit, g0(t), determined from regression analysis using PARGAN, along with the excess pinox concentration calculated using eq 4. The error bars on the kinetic limit growth rates are based on the scatter around the fit of the size distributions to the GDE. Knowledge of the condensational growth rate aids in the interpretation of the gas-phase and heterogeneous chemistry of the system, because it is proportional to the condensing vapor concentration in excess above saturation via
g0(t) )
X
β-1)φ
FIGURE 3. Particle-radius growth rate in the kinetic limit as determined from PARGAN (symbols, left-hand axis) and the pinox excess mixing ratio as determined from the chemical kinetics scheme (solid line, right-hand axis). A mass yield for pinox of 8.1% is determined by comparing these two quantities; this yield has been taken into account in the secondary y-axis values.
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vvapMW([X]∞ - [X]eq) 4FNA
(9)
where [X]∞ and [X]eq are the concentrations of the condensing vapor far away from and in equilibrium with the particle, respectively. Their difference is the driving force for condensation (or evaporation, if negative), and we call this the excess concentration (above saturation with respect to the particle phase). MW is the molecular weight of the condensing vapor, F is the particle density, and NA is Avogadro’s number. The mass yield of pinox was used as a fit parameter to produce optimal agreement between the observed and theoretical proportionality of the growth rate and excess concentration; the right-hand axis of Figure 3 has been adjusted accordingly. With the use of a particle density of 1.0 g cm-3, the resulting mass yield of condensable species is 8.1 ( 0.6%; this result is directly proportional to the assumed particle density. A molecular weight of 200 g mol-1 was assumed; the mass yield is not sensitive to this value. The effect of the molecular weight in eq 9 is to convert the molar yield in eq 4 into a mass yield. The molecular speed, vvap, also depends on molecular weight, but this appears in both eq 9 and in the condensation rate constant. These cancel if the condensation rate is near the kinetic limit and much larger than the wall loss rate; that is the case here. During the time between the end of filtering and the start of the second ozone injection (27 min), the aerosol established a new equilibrium with the gas phase. The lifetime of pinox with respect to condensation and wall loss, 1/(kcond + kwall), was less than 9 min during that time interval. Thus, the initial concentration of pinox in the afternoon should have been equal to its saturation value. For the morning experiment, however, no pinox was present when R-pinene was injected, and thus its initial concentration was zero. The fact that the
growth rate does not lag behind the pinox suggests that pinox is an immediate oxidation product and that minimal time was needed for the pinox concentration to build up to more than the saturation concentration. This indicates that saturation vapor pressure of pinox cannot be large. Equation 4 returns the excess pinox concentration above saturation, since this is what condensation depends on. For the afternoon, this is consistent with the initial (excess) concentration of zero, but for the morning, this initial value is not correct, since in fact, the initial excess concentration was negative by an unknown amount equal to the equilibrium concentration. From sensitivity studies, we know that it takes only a few minutes for the calculated morning concentration to converge with the excess concentration, due to the lifetime of condensation. All this excess concentration is available for condensation, and thus, the yield found here equals the aerosol yield. The saturation vapor pressure of some of the R-pinene oxidation products (glutaric acid, trans-norpinic acid, pinic acid, and cis-pinonic acid) has been estimated to be in the range of 0.2-5 ppbv based on measured evaporation rates (33, 34). From the near-identical relation between pinox and growth rate found for morning and afternoon, despite the difference in initial condition, we conclude that the effective saturation concentration of pinox must be at least 1 order of magnitude smaller than the lower end of that range. This suggests that other species than these may dominate the SOA formation from R-pinene or that their vapor pressures have been overestimated. Hoppel et al. (23) estimated an upper bound to the pinox saturation concentration of 10 pptv, based on an evaluation of the calculated pinox concentration, accounting for the Kelvin effect, at the onset of nucleation for a different case study. Our findings are consistent with this estimate. H2SO4 was only present in the afternoon experiment. Its mixing ratio, as calculated from eq 5, closely follows that of pinox, with mixing ratios a factor of 64 smaller (maximum H2SO4 mixing ratio is 0.8 pptv). The similar dependence of the growth rate on pinox concentration found for the morning and afternoon experiments indicates that H2SO4 did not contribute significantly to the particle growth, compared with pinox. This is reasonable, given the much smaller concentrations of H2SO4, but indicates that the mass accommodation coefficient of pinox is not dramatically smaller than that of H2SO4. 3.3. Gas-Particle Partitioning and Yield. Immediately after oxidation of the parent hydrocarbon has started, condensation can be a relatively slow process; it speeds up as more particle surface area is formed. For example, the characteristic time for the condensation of pinox (1/kcond) was 20 min at 13:30, decreasing rapidly to 3 min at 13:45 and to 1.5 min at 14:00; in contrast, it was just below 2 min at the onset of the morning experiment. The estimated characteristic time for the wall loss of pinox was 15 min. We can gain a better insight into the time-dependence of the yield by including the calculated gas-phase pinox concentration in the yield, since a large fraction of this concentration will eventually condense onto the particles. We define the condensing product yield as
Ycondense )
∆Maerosol + fcondMvapor ∆[RP]
(10)
where Mvapor is the gas-phase pinox mass concentration (in excess of saturation) and fcond is the fraction that condenses onto the particle phase (as opposed to being lost to the wall); both are determined via eq 4. This fraction was well above 90% except for the first few afternoon scans. ∆Maerosol is determined from the measured particle volume, assuming a density of 1.0 g cm-3 for the organic particulate
FIGURE 4. Aerosol mass yield as determined from the measured size distributions, corrected for wall losses. Blue solid triangles give the aerosol yield, whereas red open circles give the condensing product yield; this includes the supersaturated vapor concentration that will eventually condense. (a) Yield versus time; (b) yield versus organic aerosol mass, fitted by eq 1 (assuming one condensable product). matter. The accumulated particle volume is defined as the difference between the volume at the measurement time and the volume obtained from the scan during which the ozone injection took place (9:49 and 13:35 for morning and afternoon, respectively). The volumes were corrected for wall losses between the O3 injection time and the measurement time and calculated by numerically integrating the size distributions, excluding the largest three bins during the morning and the largest seven bins during the afternoon; the counts in those bins seemed to be entirely noise and had a disproportionate impact on the integrated volumes. Both the regular aerosol yield, Yaerosol, and the condensing product yield, Ycondense, are shown in Figure 4a versus time and in Figure 4b versus organic aerosol mass (solid triangles). Error bars are omitted for clarity. During the morning, pinox condensed only on pre-existing particles, as opposed to the afternoon, when it also condensed on small freshly nucleated particles. Immediately following nucleation, a significant portion of the particulate pinox mass was below the minimum detectable size of the scanning mobility particle sizer and is therefore not yet included in the measured aerosol yield. This could explain a considerable part of the remaining time delay in reaching the asymptotic yield for the afternoon. Only a relatively small role is left for the aerosol mass in potentially VOL. 41, NO. 17, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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influencing the observed change of the yield with time and mass. Both aerosol yields (excluding and including the contribution from the condensing vapor) have been fitted by eq 1 (Figure 4b). The one-component fit gives a ) 6.6 ( 0.6% and K ) 1.9 ( 1.1 m3 µg-1 for the former (aerosol yield) and a ) 5.8 ( 0.5% and K ) 22 ( 50 m3 µg-1 for the latter (condensing product yield). Error estimates are based on the scatter around the fit. The two-component fits are hardly distinguishable from these. When the contribution of the condensing vapor is excluded, eq 1 provides a visually compelling fit. However, by using these fit parameters, the reason for the observed dependency of the yield on time could be misinterpreted to be solely due to the organic aerosol mass, while in fact a significant portion of this dependency is due to the time needed for nucleation and condensation. The partitioning coefficient found by fitting the aerosol yield is equivalent to a saturation vapor pressure of 65 pptv; this is much higher than the estimate of Hoppel et al. (23). An upper limit to the vapor pressure of 20 pptv, found from fitting the condensing product yield with an assumed molecular weight of MW ) 200 g mol-1, is consistent with the earlier result. The kinetic limitation to gas-to-particle conversion, as found in this study, means that equilibrium approaches are not necessarily applicable to describe the aerosol formation in time, even when first-generation oxidation products partition to the aerosol phase. The difference in yield found from the growth rate analysis (8.1 ( 0.6%; section 3.2) and from the added aerosol volume (6.2 ( 0.8%; this section) appears to be partly due to the differing treatments of wall loss of condensable vapor. Also, both estimates are influenced by the variability (whether real or due to noise) in the size distributions, though in different ways: The growth rate analysis depends mostly on the shape of the number distribution, while the regular determination of yield depends on the total particle volume and is thus more sensitive to larger particles, for which the counting statistics are inferior. Combining these results, we estimate the aerosol yield for these experimental conditions to be 7 ( 1%. Both yield estimates are directly proportional to the assumed density of the organic particulate matter. The yield is dependent on experimental conditions, which makes a direct comparison with other studies difficult. However, our estimate is of comparable magnitude to those of other ozonolysis studies for similarly low organic aerosol mass (23, 35). These other studies did not use seed aerosol. Therefore, the similar values of the yield suggest that the presence of seed aerosol in our study did not significantly affect the yield. 3.4. Determination of the Particle Nucleation Rate. The nucleation rates for the afternoon experiment are shown in Figure 5. Note that these are formation rates of 1 nm particles, determined by following the evolution of the measured size distribution backward in time. Each symbol in Figure 5 is based on the particle number measured at a later time in a certain size bin (see eq 3 of the Supporting Information). The calculated H2SO4 mixing ratios are shown on the same graphs for comparison. Nucleation rates of up to 500 cm-3 s-1 were determined, while maximum H2SO4 and pinox mixing ratios were 0.8 and 50 pptv, respectively. Both vapor concentrations evolve similarly, while the nucleation rate also exhibits a similar trend, with its maximum within 2 min of the maximum vapor concentrations. This provides confidence in the internal consistency of the calculations, since a systematic error would likely have caused these not to match up. However, the data here are inconclusive as to which is the key species for nucleation. The data in Figure 5 are consistent with a second-order dependence of nucleation rate on [H2SO4] with a rate constant of about 1 × 10-12 cm3 s-1. This is comparable to rate 6050
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FIGURE 5. Nucleation rates (colored symbols) determined from size distribution data using PARGAN. Color of symbol indicates the magnitude of extrapolation, i.e., the time between nucleation and measurement. H2SO4 mixing ratios (solid line) are calculated from the chemical kinetics scheme. expressions deduced from field data (36). However, this result is highly uncertain since it is very sensitive to slight shifts in the nucleation time. We have previously used this method to determine nucleation rates for a SO2 photo-oxidation experiment in the same chamber (22); the nucleation rates found here are 11/2 to 2 times higher, while the calculated H2SO4 concentrations are a factor of 10 lower and a small amount of seed aerosol was present. There is strong evidence (23, 25, 37, 38) that H2SO4 is the main species responsible for nucleation, but it has been suggested that, in the presence of H2SO4, organics may enhance the nucleation rate (39). Our results support this hypothesis.
Acknowledgments This work was funded by the Canadian Foundation for Climate and Atmospheric Science, by the Natural Sciences and Engineering Research Council, and by the EU project Eurochamp. We thank U. Baltensperger, J. Dommen, C. Marcolli, and T. Peter for useful discussions.
Supporting Information Available Mathematical model description in PDF format. This material is available free of charge via the Internet at http:// pubs.acs.org.
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Received for review January 31, 2007. Revised manuscript received June 28, 2007. Accepted July 3, 2007. ES070245C
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