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Abstract Nucleation and subsequent growth of new aerosol particles in the atmosphere is a major source of cloud condensation nuclei and persistent large uncertainty in climate models. Newly formed particles need to grow rapidly to avoid scavenging by pre-existing aerosols and become relevant for the climate and air quality. In the continental atmosphere, condensation of oxygenated organic molecules is often the dominant mechanism for rapid growth. However, the huge variety of different organics present in the continental boundary layer makes it challenging to predict nanoparticle growth rates from gas-phase measurements. Moreover, recent studies have shown that growth rates of nanoparticles derived from particle size distribution measurements show surprisingly little dependency on potentially condensable vapors observed in the gas phase. Here, we show that the observed nanoparticle growth rates in the sub-10 nm size range can be predicted in the boreal forest only for springtime conditions, even with state-of-the-art mass spectrometers and particle sizing instruments. We find that, especially under warmer conditions, observed growth is slower than predicted from gas-phase condensation. We show that only a combination of simple particle-phase reaction schemes, phase separation due to non-ideal solution behavior, or particle-phase diffusion limitations can explain the observed lower growth rates. Our analysis provides first insights as to why atmospheric nanoparticle growth rates above 10 nm h⁻¹are rarely observed. Ultimately, a reduction of experimental uncertainties and improved sub-10 nm particle hygroscopicity and chemical composition measurements are needed to further investigate the occurrence of such a growth rate-limiting process. 

Abstract. Discerning mechanisms of sulfate formation during fine-particle pollution (referred to as haze hereafter) in Beijing is important for understanding the rapid evolution of haze and for developing cost-effective air pollution mitigation strategies. Here we present observations of the oxygen-17 excess of PM_2.5 sulfate (Δ¹⁷O(SO₄²⁻)) collected in Beijing haze from October 2014 to January 2015 to constrain possible sulfate formation pathways. Throughout the sampling campaign, the 12-hourly averaged PM_2.5 concentrations ranged from 16 to 323µg m⁻³ with a mean of (141  ±  88 (1σ))µg m⁻³, with SO₄²⁻ representing 8–25% of PM_2.5 mass. The observed Δ¹⁷O(SO₄²⁻) varied from 0.1 to 1.6‰ with a mean of (0.9  ±  0.3)‰. Δ¹⁷O(SO₄²⁻) increased with PM_2.5 levels in October 2014 while the opposite trend was observed from November 2014 to January 2015. Our estimate suggested that in-cloud reactions dominated sulfate production on polluted days (PDs, PM_2.5  ≥  75µg m⁻³) of Case II in October 2014 due to the relatively high cloud liquid water content, with a fractional contribution of up to 68%. During PDs of Cases I and III–V, heterogeneous sulfate production (P_het) was estimated to contribute 41–54% to total sulfate formation with a mean of (48  ±  5)%. For the specific mechanisms of heterogeneous oxidation of SO₂, chemical reaction kinetics calculations suggested S(IV) ( = SO₂ ⚫H₂O+HSO₃⁻  +  SO₃²⁻) oxidation by H₂O₂ in aerosol water accounted for 5–13% of P_het. The relative importance of heterogeneous sulfate production by other mechanisms was constrained by our observed Δ¹⁷O(SO₄²⁻). Heterogeneous sulfate production via S(IV) oxidation by O₃ was estimated to contribute 21–22% of P_het on average. Heterogeneous sulfate production pathways that result in zero-Δ¹⁷O(SO₄²⁻), such as S(IV) oxidation by NO₂ in aerosol water and/or by O₂ via a radical chain mechanism, contributed the remaining 66–73% of P_het. The assumption about the thermodynamic state of aerosols (stable or metastable) was found to significantly influence the calculated aerosol pH (7.6  ±  0.1 or 4.7  ±  1.1, respectively), and thus influence the relative importance of heterogeneous sulfate production via S(IV) oxidation by NO₂ and by O₂. Our local atmospheric conditions-based calculations suggest sulfate formation via NO₂ oxidation can be the dominant pathway in aerosols at high-pH conditions calculated assuming stable state while S(IV) oxidation by O₂ can be the dominant pathway providing that highly acidic aerosols (pH ≤ 3) exist. Our local atmospheric-conditions-based calculations illustrate the utility of Δ¹⁷O(SO₄²⁻) for quantifying sulfate formation pathways, but this estimate may be further improved with future regional modeling work.