## Abstract

Nucleation is a fundamental step in atmospheric new-particle formation. However, laboratory experiments on nucleation have systematically failed to demonstrate sulfuric acid particle formation rates as high as those necessary to account for ambient atmospheric concentrations, and the role of sulfuric acid in atmospheric nucleation has remained a mystery. Here, we report measurements of new particles (with diameters of approximately 1.5 nanometers) observed immediately after their formation at atmospherically relevant sulfuric acid concentrations. Furthermore, we show that correlations between measured nucleation rates and sulfuric acid concentrations suggest that freshly formed particles contain one to two sulfuric acid molecules, a number consistent with assumptions that are based on atmospheric observations. Incorporation of these findings into global models should improve the understanding of the impact of secondary particle formation on climate.

Nucleation of particles in the atmosphere has been observed to be strongly dependent on the abundance of sulfuric acid (H_{2}SO_{4}) (*1*–*4*). Sulfur dioxide (SO_{2}), the precursor of H_{2}SO_{4}, has both natural and anthropogenic sources. Anthropogenic SO_{2} emissions can have large indirect effects on climate if H_{2}SO_{4} is responsible for atmospheric nucleation, but laboratory experiments have systematically failed to reproduce ambient new-particle formation rates as well as the nucleation rate dependence on the H_{2}SO_{4} concentration (Table 1) (*5*–*15*).

Reasons for these apparent differences have been unclear. Berndt *et al*. (*5*) reported laboratory experiments with nucleation occurring at nearly ambient concentrations of H_{2}SO_{4} (10^{7} molecules cm^{−3}), whereas other experiments (performed with H_{2}SO_{4} produced from a liquid sample) have, until now, required much higher onset vapor concentrations (~10^{9} molecules cm^{−3}) (*6*–*9*). This observation revived an old idea (*11*) that other compounds, such as HSO_{5}, that were formed in the OH + SO_{2} reaction were responsible for nucleation (*13*). Recent experiments (*14*, *15*) with in situ–produced H_{2}SO_{4} have also been used to support the idea that the nature of the nucleating species can differ from H_{2}SO_{4}.

Even though nucleation has been observed to occur just slightly above ambient atmospheric H_{2}SO_{4} concentrations (*5*), none of the experiments performed to date have succeeded in producing the atmospherically relevant relation (“slope”) between the nucleation rate (*J*) and H_{2}SO_{4} concentration. This slope, according to nucleation theorem, corresponds to the number of molecules in critical cluster (*16*, *17*): *n*_{crit} = d(ln*J*)/d(ln[H_{2}SO_{4}]). Atmospheric observations (*2*–*4*) suggest this slope to be between 1 and 2. In contrast, the slopes obtained from the previous laboratory experiments (*5*–*15*) are in the range of 2 to 21.

Here, we report observations of H_{2}SO_{4} nucleation in the presence of water vapor for ambient H_{2}SO_{4} concentrations starting from 10^{6} molecules cm^{−3}. Experiments were performed in the Leibniz-Institute for Tropospheric Research laminar flow tube (IfT-LFT) and in the Finnish Meteorological Institute (FMI) laminar flow tube (*17*). We used a chemical ionization mass spectrometer (CI-MS) (*18*) for H_{2}SO_{4} measurements, a modified pulse height–analyzing ultrafine-condensation particle counter (PHA-UCPC) (*19*), and a mixing type particle-size magnifier (PSM) (*17*, *20*) for detecting particles down to ~1.3 to 1.5 nm in mobility-equivalent diameter (~1.0 to 1.2 nm mass diameter). With these instruments, a direct comparison with field measurements becomes possible because field observations typically apply a CI-MS for the H_{2}SO_{4} measurement and because nucleation rates calculated from field data are given for particles with a mass diameter of 1 nm (*2*–*4*), which is close to our estimated smallest detectable particle size.

The growth rate of freshly nucleated particles because of H_{2}SO_{4} condensation close to ambient concentrations is assumed to be small: ~1.5 nm h^{−1} at [H_{2}SO_{4}] = 10^{7} molecules cm^{−3} (*21*). Even in the atmosphere, where several condensing vapors obviously participate in the growth process, total growth rates typically do not exceed 20 nm h^{−1} (*22*). Exceptions are coastal areas, where oxidation of iodine-containing organic vapors can rapidly produce large amounts of condensable matter (*23*), and also highly polluted environments of megacities (*24*). In order to grow nucleated particles from ~1 to 3 nm, which is the lowest detection limit of modern commercial condensation particle counters, high H_{2}SO_{4} concentration and long growth times are required.

The detection efficiency of the present modified PHA-UCPC for <2-nm-diameter particles is several orders of magnitude higher than that of the state-of-art commercial particle counters (*19*). The PHA-UCPC allows also the determination of the particle size and the detection efficiency with which the particles are counted. Particles that are <2 nm in diameter are detected also with the PSM with an efficiency close to unity, allowing us to meet the challenge of slow growth. Figure 1 shows an example of a measurement series using three different counters: a commercial TSI-3025A condensation particle counter (CPC) (with a stated 50% detection limit of 3 nm) (TSI, St. Paul, MN), PHA-UCPC, and PSM. In the case of the PHA-UCPC, both raw data and detection efficiency–corrected data are depicted. The experiment was performed in the IfT-LFT using in situ–produced H_{2}SO_{4}. Within the residence time of 115 s, only a tiny fraction of particles grow to sizes detectable with the TSI-3025A CPC, which is a commonly used instrument in nucleation studies. The use of an improper counter clearly affects the apparent onset H_{2}SO_{4} concentration needed for nucleation and also the slope d(ln*N*)/d(ln[H_{2}SO_{4}]), where *N* is the observed particle number concentration.

Nucleation rates obtained from different experiments are presented in Fig. 2. All series show similar behavior. For photolysis experiments, the H_{2}SO_{4} concentrations are average concentrations from kinetic modeling (*12*). End concentrations measured with the CI-MS matched the modeled end concentrations well, with only some minor deviations for high concentrations and long residence times (fig. S1) (*17*). In the case of the H_{2}SO_{4} from the liquid sample, the initial concentration measured by the CI-MS is shown. Separate fittings of ln(*J*) versus ln([H_{2}SO_{4}]) to different data series (Fig. 2) yield slopes between 1.0 and 2.1, with an average value of 1.5. This is, to our knowledge, the first time that nucleation of H_{2}SO_{4} from a liquid sample has been reported at concentrations in the range of 10^{7} to 10^{8} molecules cm^{−3}. This is also the first experiment showing the atmospherically relevant slope. It should be noted that in the experiment performed with the FMI laminar flow tube, the temperature was 25°C and relative humidity (RH) was 30%, whereas the IfT-LFT experiments were performed at the temperature of 20°C and RH of 22%. A 5°C higher temperature can probably explain the slightly smaller nucleation rates in the FMI experiment.

A slope of 2 can be explained by collision-controlled or kinetic nucleation (*10*), in which *J = K*[H_{2}SO_{4}]^{2}, where *K* is the kinetic coefficient. A slope of unity might, however, require an additional stabilizing and/or condensing vapor participating in the initial growth of the H_{2}SO_{4} clusters, under the assumption that the role of water condensation is small. The slope of unity can also be explained by the activation of existing clusters (*25*), described by *J = A*[H_{2}SO_{4}], where *A* is the activation coefficient, but we had no indication of preexisting clusters or gaseous impurities in our experiment (*17*). Application of kinetic or activation nucleation theory to our IfT data yields prefactor values of *K* ≈ 5 × 10^{−14} cm^{3} s^{−1} and *A* ≈ 3 × 10^{−6} s^{−1}. This is consistent with ambient data, in which *K* ranges from 10^{−14} to 10^{−11} cm^{3} s^{−1} (*2*–*4*) and *A* ranges between 10^{−7} and 10^{−5} s^{−1} (*2*, *4*).

The growth of the nucleated particles was also investigated. Figure 3 shows the mean particle diameter (*d*_{p}) determined with the PHA-UCPC for the photolysis experiments as a function of H_{2}SO_{4} concentration for four different residence times. For comparison, the data taken with a commonly used differential mobility particle sizer (DMPS) system (with a TSI-3025A CPC) are also depicted. From the linear fittings to the data, we get an estimate of the growth rate, which is (6 ± 2) × 10^{−11} [H_{2}SO_{4}] cm^{3} molecule^{−1} nm s^{−1}. Theoretically, the growth rate from pure H_{2}SO_{4} condensation at ~2-nm particle sizes is ~4 × 10^{−11} [H_{2}SO_{4}] cm^{3} molecule^{−1} nm s^{−1} (*21*). The agreement can be considered good, and the small difference between measurement and theory can possibly be explained by co-condensation of water. Thus, additional condensing vapors are not necessarily needed to explain the growth in our experiments. The particle diameter after growth represents the sum of the diameter of critical cluster (*d*_{0}) and the contribution of growth. The fittings (Fig. 3) intercept the mobility diameter axis at the size *d*_{0}, suggesting a critical cluster diameter of (1.2 ± 0.2) nm, which corresponds to a mass diameter of (~0.9 ± 0.2) nm (*26*). However, it should be noted that the PHA-UCPC calibration is based on charged particles, and thus, because of the neutrality of the investigated particles, an additional positive error of ~0.3 nm can be assumed (*17*), yielding the final estimate of the critical cluster mass diameter as ~0.7 to 1.4 nm. The lower limit of this estimation corresponds to approximately 200 atomic mass units (*26*). This is reasonably well in line with our observed slope, which suggests that critical cluster probably contains up to two molecules of H_{2}SO_{4}. Furthermore, the size of critical clusters observed in our experiment is about the same as the starting size in atmospheric nucleation events (*27*).

Our experimental results regarding the onset–sulfuric acid concentration as well as the slopes for H_{2}SO_{4} from the liquid sample are clearly in contradiction with other studies performed to date. A probable explanation for the disagreement is as follows. Our data show that high concentrations of H_{2}SO_{4} and proper residence time are needed to allow the particles to grow to ~3 nm in diameter, which is the lowest detection limit of commercial CPCs. The detection efficiency curve of a CPC is typically very steep close to the 50% cutsize of the detector and therefore very sensitive to particle size. According to our data at RH = 22%, the growth rate was ~6 × 10^{−11} [H_{2}SO_{4}] cm^{3} molecules^{−1} nm s^{−1}, which provides evidence that without a suitable detector and long residence times the growth of the freshly nucleated particles is not efficient enough so that they can be observed at [H_{2}SO_{4}] below ~10^{8} to 10^{9} molecules cm^{−3} (Fig. 3). For the most experiments performed to date, the insufficient growth rate together with insufficient counting efficiency can explain a large fraction of the discrepancy between those and our present study. To summarize, it is possible that all of the experiments cited here (including our earlier studies) have been affected either by a short residence time, size-sensitive counting efficiency of particle detectors, unexpected additional loss of H_{2}SO_{4}, or all of the above.

Explanation for the mysterious disagreement between experiments performed with in situ–produced H_{2}SO_{4} (*5*) and H_{2}SO_{4} from a liquid sample (*6*–*9*) lies at least partly in the different H_{2}SO_{4} profiles. Because of nearly uniform H_{2}SO_{4} concentrations in case of in situ experiments (*5*, *12*, *13*), particles have much more time to grow to detectable sizes. In the case of a point source, [H_{2}SO_{4}] decreases rapidly with time (fig. S3) (*17*), and the growth is not efficient enough. We have conducted experiments with these two approaches by using the same flow tube and detectors. Therefore, the differences arising from different experimental geometries and different detectors are eliminated in our study.

In conclusion, we have shown that the mystery concerning the apparent disagreement of several orders of magnitude in the nucleation rates and 2 to 3 orders of magnitude in the onset [H_{2}SO_{4}] between the in situ–produced H_{2}SO_{4} and the H_{2}SO_{4} from a liquid sample does not exist. Therefore, the role of other sulfur-containing species (*13*), like HSO_{5}, seems to be of minor importance in the nucleation process, even though these other pathways cannot be completely excluded. Furthermore, we showed that nucleation occurs at atmospherically relevant H_{2}SO_{4} concentrations. The relation between the nucleation rate and H_{2}SO_{4} concentration [d(ln*J*)/d(ln[H_{2}SO_{4}]) = 1.0 to 2.1] from our experiment is consistent with the corresponding atmosphere observations. A nucleation rate of unity is observed at a [H_{2}SO_{4}] slightly above 10^{6} molecules cm^{−3}, which is well in line with most atmospheric data (*1*–*4*, *28*, *29*). However, in certain locations co-occurrence of nucleation mechanisms involving other species is plausible. We also showed that H_{2}SO_{4} condensation has a dominating contribution to the observed particle growth in our experiment. The growth rate of (6 ± 2) × 10^{−11} [H_{2}SO_{4}] cm^{3} molecules^{−1} nm s^{−1} obtained from our data is close to the theoretical estimate of pure H_{2}SO_{4} condensation and is smaller than ambient growth rates, which supports the findings that in the atmosphere, compounds like organics (*30*, *31*) or ammonia (*32*) are involved in the early growth process. Even though the exact nucleation mechanism remains an open question, our results show that H_{2}SO_{4} at atmospheric concentrations can explain atmospheric nucleation rates in most locations even without clear participation of ammonia or organic substances. Therefore, our findings can be used straightforwardly in further model studies, including climate models.

## Supporting Online Material

www.sciencemag.org/cgi/content/full/327/5970/1243/DC1

Materials and Methods

SOM Text

Figs. S1 to S4

## References and Notes

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- We thank K. Pielok and A. Rohmer for technical assistance and J. Heitzenberg, K.E.J. Lehtinen, V.-M. Kerminen, and M. McGrath for help preparing the manuscript. C. D. O’Dowd is acknowledged for providing the PHA-UCPC instrument. K. Lehtipalo is acknowledged for assistance with the PHA-UCPC, J. Mikkilä and E. Siivola for constructing the PSM, R. Taipale for help with the PTR-MS, J. Hakala and K. Neitola for assistance with experiments, and T. Nieminen for useful discussions. This work was partially funded by European Commision 6th Framework program project European Integrated Project on Aerosol, Cloud, Climate, and Air Quality Interactions (EUCAARI), contract 036833-2. Financial support from Kone foundation, Väisälä foundation, Otto Malm foundation, the Academy of Finland and European Research Council is acknowledged.