New particle formation (NPF) is closely related to atmospheric environment. It is a common atmospheric phenomenon, which has been observed all over the world (Kulmala et al., 2004). High concentrations of ultrafine particles are formed intensively during NPF events. It has been illustrated through both theoretical modeling and field observations that these ultrafine particles can grow and serve as cloud condensation nuclei (Kuang et al., 2009; Spracklen et al., 2008) and thus affect climate (IPCC, 2013). The increased number concentration of ultrafine particles also raises concerns about human health (HEI, 2013).

New particles are formed by nucleation from gaseous precursors, such as sulfuric acid, ammonia, and organics. Newly formed particles either grow by condensation or are lost by coagulation with other particles (McMurry, 1983). Aerosol Fuchs surface area, AFuchs, is a parameter that describes the coagulation scavenging effect quantitatively. In addition to gaseous precursors participating in nucleation and subsequent condensational growth, there has been a consensus that the occurrence of a NPF event is also limited by AFuchs, because the survival possibility of nucleated particles is suppressed when the coagulation scavenging effect is significant (Weber et al., 1997; Kerminen et al., 2001; Kuang et al., 2012). Reported average AFuchs (or in the form of a condensation sink) on NPF days was found to be lower than that on non-event days at several locations (Dal Maso et al., 2005; Gong et al., 2010; Qi et al., 2015).

A dimensionless criterion, LΓ, was proposed to characterize the ratio of particle scavenging loss rate over condensational growth rate, and to predict the occurrence of NPF events in diverse atmospheric environments (Kuang et al., 2010). By definition, LΓ is determined by three factors, i.e., the sulfuric acid concentration, the growth enhancement factor representing contributions of other gaseous precursors in addition to the sulfuric acid concentration, Γ, and AFuchs. The diurnal sulfuric acid concentration can vary drastically due to the substantial change in radiation (e.g., from several thousand to ∼ 1.5×106# cm-3 in this campaign) and the increase in sulfuric acid concentration after the sunrise can potentially lead to nucleation. The values of AFuchs, however, were usually reported within a narrow range at locations, such as Tecamac, Atlanta, and Boulder (Kuang et al., 2010). The sulfuric acid concentration in Atlanta and Hyytiälä can differ significantly among days (Eisele et al., 2006; Petäjä et al., 2009). Therefore, the sulfuric acid concentration often governs nucleation and subsequent growth in the sulfur-rich atmosphere, such as in Atlanta (McMurry et al., 2005). The growth enhancement factor, Γ, at Hyytiälä varied in a wide range, while those at Tecamac and Boulder were found in a relatively narrow range.

Aerosol concentrations in Beijing are usually much higher than those in clean environments. The annual average PM2.5 mass concentration in 2016 was 73 µg m-3 (reported by the Beijing Municipal Environmental Protection Bureau), and the average AFuchs measured in Beijing by this campaign was 381.5 µm2 cm-3, which is approximately a magnitude higher than those measured in clean environments, such as in Hyytiälä (Dal Maso et al., 2002). Differently from the comparatively slow accumulation and depletion process of aerosol concentrations in clean environments, AFuchs in Beijing may change rapidly because of changes in air mass origins (Wehner et al., 2008) or accumulation of pollutants.

The sulfuric acid concentration is needed to estimate LΓ and direct measurement of particle size distribution down to ∼ 1 nm will help to better quantify NPF events. Although sulfuric acid has been measured around the world (Erupe et al., 2010) and analyses based on sub-3 nm size distributions have been conducted sporadically since the development of diethylene glycol scanning mobility particle spectrometers (DEG-SMPS, Jiang et al., 2011a, b; Kuang et al., 2012) and particle size magnifiers (PSMs, Vanhanen et al., 2011; Kulmala et al., 2013), there are limited data on atmospheric sulfuric acid concentrations and directly measured sub-3 nm particle size distributions in China. A campaign in Beijing during the 2008 Olympic Games (Yue et al., 2010; Zheng et al., 2011) characterized atmospheric sulfuric acid concentration and its correlation with the new particle formation rate. The exponent in the correlation of the formation rate, J3, with the sulfuric acid concentration was found to be 2.3. The exponent for correlating derived J1.5 with the sulfuric acid concentration was 2.7 (Wang et al., 2011). They were different from the exponents between 1 and 2 often reported in other places around the world (Riipinen et al., 2007; Sihto et al., 2006; Kuang et al., 2008). The same instrument used in the Beijing campaign was also deployed in Kaiping to measure the sulfuric acid concentration during a 1-month campaign in 2008 (Wang et al., 2013a). Sub-3 nm particle size distributions have not been reported previously in China, except for the 1–3 nm particle number concentration in Shanghai in the winter of 2013 inferred by a PSM (Xiao et al., 2015). Due to the limitation of observation data, although a good correlation between the new particle formation rate and the sulfuric acid concentration in Beijing was found and the ratio of the sulfuric acid concentration over AFuchs was reported to positively correlate with the number concentration of 3–6 nm particles (Wang et al., 2011), the roles of the sulfuric acid concentration and AFuchs in determining the occurrence of NPF events have not been quantitatively illustrated.

In this study, we aimed to examine the roles of AFuchs and the sulfuric acid concentration in determining whether a NPF event will occur on a particular day in Beijing. The data analysis was based on simultaneous measurement of particle size distributions down to ∼ 1 nm and sulfuric acid. The correlation between particle formation rate, J1.5, and the sulfuric acid concentration was examined. LΓ was used to predict the occurrence of NPF events. Daily variations of the three parameters determining LΓ, i.e., the sulfuric acid concentration, Γ, and AFuchs, were compared. A nominal value of AFuchs was suggested to predict the occurrence of NPF events in Beijing. The relationship between the PM2.5 mass concentration and NPF events was also examined.

A field campaign studying NPF in Beijing was carried out from 7 March 2016 to 7 April 2016. The campaign site was located on the campus of Tsinghua University. Details of this site can be found elsewhere (Cai and Jiang, 2017; He et al., 2001). A home-made DEG SMPS was used to measure sub-5 nm particle size distributions and a particle size distribution system (including a TSI aerodynamic particle sizer and two parallel SMPSs, equipped with a TSI nanoDMA and a TSI long DMA, respectively) was used to measure size distributions of particles from 3 nm (in electrical mobility diameter) to 10 µm (in aerodynamic diameter, Liu et al., 2016). A specially designed miniature cylindrical differential mobility analyzer (mini-cyDMA) for effective classification of sub-3 nm aerosol was equipped with the DEG-SMPS (Cai et al., 2017). A cyclone was used at the sampling inlet to remove particles larger than 10 µm. The sampled aerosol was subsequently dried by a silica-gel diffusion drier. The diameter change due to drying was neglected when calculating AFuchs since the mean daytime relative humidity during the campaign period was ∼ 25 %. Diffusion losses, charging efficiency, penetration efficiencies through the DMAs, detection efficiencies of particle counters, and multi-charging effect were considered during data inversion. The particle density was assumed to be 1.6 g cm-3 according to local observation results (Hu et al., 2012).

Sulfuric acid was measured by a modified high-resolution time-of-flight chemical ionization mass spectrometer (HR-ToF-CIMS, Aerodyne Research Inc.). Instead of using a radioactive ion source, a home-made corona discharge (CD) ion source was utilized with the HR-TOF-CIMS. The CD ion source was designed to be able to operate from a few Torr up to near atmospheric pressure and has been successfully implemented in measuring ambient amine (Zheng et al., 2015a) and formaldehyde (Ma et al., 2016). In this study, nitrate reagent ions were used to measure gaseous sulfuric acid (Zheng et al., 2010). The detailed ion chemistry to generate nitrate ions and the calibration procedure for sulfuric acid measurement have been reported in Zheng et al. (2015b). Ambient sulfuric acid concentration in Beijing has been reported only once in a field campaign conducted in 2008 (Zheng et al., 2011; Wang et al., 2011). Compared to that campaign, the sulfuric acid concentration measured in this study displayed similar diurnal variations, but with lower daily-maximum values. This might be caused by the relatively weak solar radiation intensity encountered in this springtime observation compared with the previous summertime campaign. To verify the precision of sulfuric acid measurement, the instrument was calibrated daily at night and background checks were performed for ∼ 3 min each hour during daytime.

A meteorological station (Davis 6250) measuring temperature, relative humidity, wind speed, wind direction, and precipitation was located ∼ 10 m away from the sampling inlet. The PM2.5 mass concentration measured in the nearest national monitoring station (Wanliu station, ∼ 5 km away to the southwest of our campaign site) was also used for analysis. Backward trajectories were obtained from the online HYSPLIT server of the National Oceanic and Atmospheric Administration (NOAA).

Nucleation is only the first step of new particle formation. The random collisions of gaseous precursor molecules can form clusters together by Van der Waals forces and/or chemical bonds. These clusters become particles if they are more likely to grow by condensation rather than evaporate. However, particles formed by nucleation may be scavenged through coagulation with larger particles before they grow large enough to be detected (McMurry, 1983; Zhang et al., 2012). Nucleation only refers to the process where stable molecular clusters formed spontaneously from gaseous precursors. New particle formation also requires subsequent condensational growth of freshly nucleated particles. That is, the occurrence of nucleation is mainly determined by gaseous precursors (e.g., sulfuric acid and organics) in atmospheric environments, while new particle formation is also influenced by the coagulation scavenging effect of pre-existing aerosols. A possibility exists that nucleation occurs while NPF events are not observed because of the short lifetime of nucleated particles due to a strong coagulation scavenging (Kerminen et al., 2001). In fact, nucleation can also be suppressed when the aerosol concentration is high since vapors and clusters may also be scavenged by aerosol surfaces.

Aerosol Fuchs surface area, AFuchs, is a representative parameter of coagulation scavenging based on kinetic theory. It is corrected for particles whose size falls in the transition regime (Davis et al., 1980; McMurry, 1983). The formula assuming a unity mass accommodation coefficient (sticking probability) is shown in Eq. (1), AFuchs=4π3∫dmin∞dp2×Kn+Kn21+1.71Kn+1.33Kn2×n×ddp, where dp is the particle diameter, dmin is the smallest particle diameter in theory and the smallest detected one in practice, Kn is the Knudsen number, and n is the particle size distribution function, dN/ddp. The condensation sink and coagulation sink can also describe how rapidly gaseous precursors and particles are scavenged by pre-existing aerosols, respectively (Kerminen et al., 2001; Kulmala et al., 2001). Since the condensation sink is proportional to AFuchs (McMurry et al., 2005) and the coagulation sink can be approximately converted to the condensation sink using a simple formula (Lehtinen et al., 2007), only AFuchs is used in this study to describe the coagulation scavenging effect. Condensation sink values reported in previous studies are referred to in the form of AFuchs. The diffusion coefficient of sulfuric acid was assumed to be 0.117 cm-2 s-1 (Gong et al., 2010) when converting the condensation sink into AFuchs.

A dimensionless criterion, LΓ, was proposed to predict the occurrence of NPF events (Kuang et al., 2010). It is defined as LΓ=c‾×AFuchs4β11N1×1Γ, where c‾ is the mean thermal speed of sulfuric acid that can be calculated from molecular kinetic theory; β11 is the coagulation coefficient between sulfuric acid monomers that can be calculated using Eq. (13.56) in Seinfeld and Pandis (2006); N1 is the number concentration of sulfuric acid; Γ is a growth enhancement factor and is defined as Γ=2GRv1Nmc‾, where GR is the observed mean growth rate; v1 is the corresponding volume of sulfuric acid monomer and was estimated to be 1.7×10-28 m3 (the volume of a hydrated sulfuric acid molecule, Kuang et al., 2010); and Nm is the maximum number of sulfuric acid concentration during a whole NPF event period. Since other gaseous precursors in addition to sulfuric acid might also contribute to the condensational growth of particles formed by nucleation (O'Dowd et al., 2002; Ristovski et al., 2010) and only sulfuric acid concentration is used in Eq. (2), the ratio of measured growth rate over the sulfuric acid condensational growth rate (Weber et al., 1997), i.e., Γ, was used for correction. It should be clarified that LΓ in Eq. (2) is defined similarly to that in McMurry et al. (2005) but slightly differently from that in Kuang et al. (2010), since LΓ in this study presents time-resolved values rather than event-specific ones. Theoretically, Γ can also be time- and size-resolved when using time- and size-resolved GR and time-resolved sulfuric acid (Kuang et al., 2012). However, Γ during each NPF event is assumed to be constant in Eq. (3) because further evaluations are needed for this time- and size-resolved model. Note that in Eq. (2) the absolute sulfuric acid concentrations were effectively normalized by the corresponding daily-maximum sulfuric acid concentrations and thus have no influence on LΓ values and conclusions based on LΓ reported in this study.

A new balance formula to estimate the new particle formation rate was proposed recently (Cai and Jiang, 2017) and is given below: Jk=dN[dk,du)dt+∑dg=dkdu-1∑di=dmin⁡+∞βi,gN[di,di+1)N[dg,dg+1)-12∑dg=dmindu-1∑di3=max(dmin3,dk3-dmin3)di+13+dg+13≤du3β(i,j)N[di,di+1)N[dg,dg+1)+nu×GRu, where Jk is the formation rate of particles at the size of dk, N[dk,du) is the total number concentration of particles from dk to du (not included), du is the upper bound of the size range for calculation (25 nm in this study), du-1 is the lower bound of the last size bin, and dmin is the size of the smallest cluster in theory and the smallest detected size in practice (1.3 nm in this study). The second and third terms on the right-hand side of Eq. (4) are the coagulation sink term (CoagSnk) and the coagulation source term (CoagSrc), respectively. The difference between CoagSnk and CoagSrc is the net CoagSnk representing the net rate of particles from dk to du, i.e., lost by coagulation scavenging. The last term is often negligible according to the determination criteria for du. dN / dt is the balance result of Jk and net CoagSnk.

A total of 26 days from 12 March to 6 April was classified by the occurrence of a daytime NPF event. A typical NPF day is featured with distinct and persisting increases in the sub-3 nm particle number concentration and subsequent growth of these nucleated particles. A non-event day means that neither of these two features was observed. As shown in Fig. 1, there are 11 typical NPF days and 13 non-event days. The other 2 days, i.e., 19 and 30 March, were classified as undefined days. On these days, the increase in the sub-3 nm particle number concentration and subsequent growth were both observed. However, the sub-3 nm particle number concentration was relatively low and the evolution of particle size distributions was not continuous. NPF events mainly occurred when wind came from northwest of Beijing and non-event days were associated with air masses from the southwest (as summarized in Table 1). Air masses coming from the north usually experience less influence from urban pollution (Wehner et al., 2008; Wang et al., 2013b); i.e., the AFuchs values on days dominated by the northerly wind are usually lower than those on days dominated by the southwesterly wind (Wu et al., 2007).

The occurrence of NPF events on most days can be predicted by LΓ if unity was empirically chosen as the threshold value. Greater LΓ indicates higher possibilities of nucleated particles being scavenged by coagulation before they can continue to grow. Growth rates on non-event days were assumed to be 2.4 nm h-1, the mean value of observed growth rates on NPF days (the range is 1.2 to 3.3 nm h-1). A threshold value of LΓ can not be theoretically predicted but can be empirically estimated; 0.7 was suggested as the threshold value by Kuang et al. (2010). However, unity suggested by McMurry et al. (2005) appeared to work better for results from this campaign in Beijing. As shown in Table 1, the median and mean values of LΓ on NPF days observed in this campaign were 0.55 and 0.71 (with a standard deviation of 0.40), respectively, compared to 3.05 and 3.45 on non-event days (with a standard deviation of 1.79), respectively. However, some exceptions were also observed. On the 2 undefined days, LΓ were 1.40 and 0.64, respectively, and weak nucleation was observed. Although the estimated LΓ value on 18 March was 1.75, a comparatively weak but still distinct NPF event was observed. Despite these few exceptions, LΓ works well on most days in this campaign and was verified in other places (Kuang et al., 2010). The following discussion is focused on the contribution of different factors, i.e., the sulfuric acid concentration, Γ, and AFuchs.

Factors governing the occurrence of NPF events in Beijing were examined using data from a field campaign during 12 March 2016 to 6 April 2016. In these 26 days, 11 typical NPF events were observed. The rest were 2 undefined days and 13 non-event days. The new particle formation rate, J1.5, had a positive correlation with the sulfuric acid concentration, with a fitted mean exponent of 2.4. However, the sulfuric acid concentrations on NPF days were not significantly higher than those on non-event days. A dimensionless criterion proposed by Kuang et al. (2010), LΓ, was found to be applicable to predict NPF events in most days. Theoretically, LΓ is determined by the sulfuric acid concentration, the enhancement factor, Γ, and the aerosol Fuchs surface area, AFuchs, together. In Beijing, however, AFuchs alone was found to be in a good correlation with LΓ (R2=0.88). Differently from NPF events observed at other locations, such as Hyytiälä, the daily-maximum sulfuric acid concentration and the enhancement factor in Beijing only varied in a narrow range with geometric standard deviations of 1.40 and 1.31, respectively, while AFuchs varied significantly among days with a geometric standard deviation of 2.56. It was inferred that the concentrations of gaseous precursors, such as sulfuric acid, in Beijing were high enough to initiate nucleation, while it was AFuchs that determined whether a NPF event would occur or not. An AFuchs value of 200 µm2 cm-3 was proposed as the empirical threshold in Beijing below which NPF events are highly likely to occur. NPF events will be suppressed when AFuchs is higher than this threshold value. The AFuchs dominated characteristics in Beijing are different from those at other locations, such as Atlanta, Boulder, and Hyytiälä. Since AFuchs in Beijing was mainly governed by accumulation mode particles (50 to 500 nm) and the normalized dAFuchs‾/dlog⁡dp in this size range was relatively stable at different AFuchs levels in Beijing, measured AFuchs had a good correlation with the PM2.5 mass concentration (R2=0.85). Accordingly, the PM2.5 mass concentration may also serve as a rough and simple parameter to predict the occurrence of NPF events in Beijing. An empirical PM2.5 threshold value of 30 µg m-3 was proposed based on data from this field campaign and was found to also work well for other field campaigns in Beijing.